diff --git a/cvat-ui/src/components/create-project-page/create-project-content.tsx b/cvat-ui/src/components/create-project-page/create-project-content.tsx
index 05c53dd85c75d003044f460786b7515dfaa3319d..52fac3c43134b6e8dd2719f7697ca8b696dd19fc 100644
--- a/cvat-ui/src/components/create-project-page/create-project-content.tsx
+++ b/cvat-ui/src/components/create-project-page/create-project-content.tsx
@@ -147,6 +147,7 @@ export default function CreateProjectContent(): JSX.Element {
             notification.info({
                 message: 'The project has been created',
                 btn,
+                className: 'cvat-notification-create-project-success',
             });
         }
 
diff --git a/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx b/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx
index 51c13cf12b6238401969aeaa95d9bffce7c50de6..7928f0be4cb65095af1b5c0706369c727f5adf4d 100644
--- a/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx
+++ b/cvat-ui/src/components/move-task-modal/label-mapper-item.tsx
@@ -45,6 +45,7 @@ export default function LabelMapperItem(props: LabelMapperItemProps): JSX.Elemen
             </Col>
             <Col>
                 <Select
+                    className='cvat-move-task-label-mapper-item-select'
                     disabled={typeof projectLabels === 'undefined'}
                     value={value.newLabelName || ''}
                     onChange={(_value) =>
diff --git a/tests/cypress/integration/actions_projects/case_94_move_task_between_projects.js b/tests/cypress/integration/actions_projects/case_94_move_task_between_projects.js
new file mode 100644
index 0000000000000000000000000000000000000000..99c5a6bd24c22a64a1c799cbc0065d38e374d172
--- /dev/null
+++ b/tests/cypress/integration/actions_projects/case_94_move_task_between_projects.js
@@ -0,0 +1,107 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+/// <reference types="cypress" />
+
+context('Move a task between projects.', () => {
+    const caseID = 94;
+    const firtsProject = {
+        name: `Firts project case ${caseID}`,
+        label: 'car',
+        attrName: 'color',
+        attrVaue: 'red',
+        multiAttrParams: false
+    }
+
+    const secondProject = {
+        name: `Second project case ${caseID}`,
+        label: 'bicycle',
+        attrName: 'color',
+        attrVaue: 'yellow',
+        multiAttrParams: false
+    }
+
+    const taskName = `Task case ${caseID}`;
+    const imagesCount = 1;
+    const imageFileName = `image_${taskName.replace(/\s+/g, '_').toLowerCase()}`;
+    const width = 800;
+    const height = 800;
+    const posX = 10;
+    const posY = 10;
+    const color = 'white';
+    const archiveName = `${imageFileName}.zip`;
+    const archivePath = `cypress/fixtures/${archiveName}`;
+    const imagesFolder = `cypress/fixtures/${imageFileName}`;
+    const directoryToArchive = imagesFolder;
+    const advancedConfigurationParams = false;
+    const forProject = true;
+    const attachToProject = false;
+    const multiAttrParams = false;
+
+    function checkTask (project, expectedResult) {
+        cy.goToProjectsList();
+        cy.openProject(project);
+        cy.get('.cvat-tasks-list-item').should(expectedResult);
+    }
+
+    before(() => {
+        cy.imageGenerator(imagesFolder, imageFileName, width, height, color, posX, posY, firtsProject.label, imagesCount);
+        cy.createZipArchive(directoryToArchive, archivePath);
+        cy.visit('/');
+        cy.login();
+    });
+
+    beforeEach(() => {
+        cy.goToProjectsList();
+        cy.createProjects(firtsProject.name, firtsProject.label, firtsProject.attrName, firtsProject.attrVaue, firtsProject.multiAttrParams);
+        cy.createProjects(secondProject.name, secondProject.label, secondProject.attrName, secondProject.attrVaue, secondProject.multiAttrParams);
+        cy.openProject(firtsProject.name);
+        cy.createAnnotationTask(
+            taskName,
+            firtsProject.label,
+            firtsProject.attrName,
+            firtsProject.attrVaue,
+            archiveName,
+            multiAttrParams,
+            advancedConfigurationParams,
+            forProject,
+            attachToProject.no,
+            firtsProject.name,
+        );
+    });
+
+    afterEach(() => {
+        cy.goToProjectsList();
+        cy.openProject(firtsProject.name);
+        cy.deleteProjectViaActions(firtsProject.name);
+        cy.openProject(secondProject.name);
+        cy.deleteProjectViaActions(secondProject.name);
+    });
+
+    describe(`Testing "Case ${caseID}"`, () => {
+        // Waiting to fix https://github.com/openvinotoolkit/cvat/issues/3281
+        it.skip('Move a task between projects from a project.', () => {
+            checkTask(secondProject.name, 'not.exist');
+            checkTask(firtsProject.name, 'exist');
+            cy.movingTask(taskName, secondProject.name, firtsProject.label, secondProject.label);
+            checkTask(firtsProject.name, 'not.exist');
+            checkTask(secondProject.name, 'exist');
+        });
+
+        it('Move a task between projects from task list.', () => {
+            cy.goToTaskList();
+            cy.movingTask(taskName, secondProject.name, firtsProject.label, secondProject.label);
+            checkTask(firtsProject.name, 'not.exist');
+            checkTask(secondProject.name, 'exist');
+        });
+
+        it('Move a task between projects from a task.', () => {
+            cy.goToTaskList();
+            cy.openTask(taskName);
+            cy.movingTask(taskName, secondProject.name, firtsProject.label, secondProject.label, true);
+            checkTask(firtsProject.name, 'not.exist');
+            checkTask(secondProject.name, 'exist');
+        });
+    });
+});
diff --git a/tests/cypress/integration/actions_projects/case_95_move_task_to_project.js b/tests/cypress/integration/actions_projects/case_95_move_task_to_project.js
new file mode 100644
index 0000000000000000000000000000000000000000..7ac0459dbf9039400938c3ac508b6bc9ea50bb46
--- /dev/null
+++ b/tests/cypress/integration/actions_projects/case_95_move_task_to_project.js
@@ -0,0 +1,77 @@
+// Copyright (C) 2021 Intel Corporation
+//
+// SPDX-License-Identifier: MIT
+
+/// <reference types="cypress" />
+
+context('Move a task to a project.', () => {
+    const caseID = '95';
+    const task = {
+        name: `Case ${caseID}`,
+        label: 'Tree',
+        attrName: 'Kind',
+        attrValue: 'Oak',
+    }
+
+    const project = {
+        name: `Case ${caseID}`,
+        label: 'Tree',
+        attrName: 'Kind',
+        attrVaue: 'Oak'
+    }
+
+    const imagesCount = 1;
+    const imageFileName = `image_${task.name.replace(' ', '_').toLowerCase()}`;
+    const width = 800;
+    const height = 800;
+    const posX = 10;
+    const posY = 10;
+    const color = 'gray';
+    const archiveName = `${imageFileName}.zip`;
+    const archivePath = `cypress/fixtures/${archiveName}`;
+    const imagesFolder = `cypress/fixtures/${imageFileName}`;
+    const directoryToArchive = imagesFolder;
+
+    before(() => {
+        cy.visit('/');
+        cy.login();
+        cy.imageGenerator(imagesFolder, imageFileName, width, height, color, posX, posY, task.name, imagesCount);
+        cy.createZipArchive(directoryToArchive, archivePath);
+    });
+
+    beforeEach(() => {
+        cy.goToTaskList();
+        cy.createAnnotationTask(task.name, task.label, task.attrName, task.attrValue, archiveName);
+        cy.goToProjectsList();
+        cy.createProjects(project.name, project.label, project.attrName, project.attrVaue);
+    });
+
+    afterEach(() => {
+        cy.goToProjectsList();
+        cy.openProject(project.name);
+        cy.deleteProjectViaActions(project.name);
+    });
+
+    describe(`Testing "Case ${caseID}"`, () => {
+        it('Move a task from task list.', () => {
+            cy.openProject(project.name);
+            cy.get('.cvat-tasks-list-item').should('not.exist');
+            cy.goToTaskList();
+            cy.movingTask(task.name, project.name, task.label, project.label);
+            cy.goToProjectsList();
+            cy.openProject(project.name);
+            cy.get('.cvat-tasks-list-item').should('exist');
+        });
+
+        it('Move a task from task.', () => {
+            cy.openProject(project.name);
+            cy.get('.cvat-tasks-list-item').should('not.exist');
+            cy.goToTaskList();
+            cy.openTask(task.name);
+            cy.movingTask(task.name, project.name, task.label, project.label, true);
+            cy.goToProjectsList();
+            cy.openProject(project.name);
+            cy.get('.cvat-tasks-list-item').should('exist');
+        });
+    });
+});
diff --git a/tests/cypress/support/commands.js b/tests/cypress/support/commands.js
index d276dd82c54cb97eca2711965251ee49577f5460..d91cfa96b5023198ab70b12a4f0b00229ef8f7af 100644
--- a/tests/cypress/support/commands.js
+++ b/tests/cypress/support/commands.js
@@ -133,7 +133,9 @@ Cypress.Commands.add(
         }
         cy.contains('button', 'Submit').click();
         if (expectedResult === 'success') {
-            cy.contains('The task has been created');
+            cy.get('.cvat-notification-create-task-success')
+                .should('exist')
+                .find('[data-icon="close"]').click();
         }
         if (!forProject) {
             cy.goToTaskList();
diff --git a/tests/cypress/support/commands_projects.js b/tests/cypress/support/commands_projects.js
index e4633160fcf562d757bd96aa17285c7e79815566..b4ab2429b3847a6143612f6be2fe18da031d6b72 100644
--- a/tests/cypress/support/commands_projects.js
+++ b/tests/cypress/support/commands_projects.js
@@ -29,9 +29,11 @@ Cypress.Commands.add(
             cy.contains('Submit').click();
         });
         if (expectedResult == 'success') {
-            cy.contains('The project has been created').should('exist');
+            cy.get('.cvat-notification-create-project-success')
+                .should('exist')
+                .find('[data-icon="close"]').click();
         } else if (expectedResult == 'fail') {
-            cy.contains('The project has been created').should('not.exist');
+            cy.get('.cvat-notification-create-project-success').should('not.exist');
         }
         cy.goToProjectsList();
     },
@@ -90,3 +92,35 @@ Cypress.Commands.add('closeNotification', (className) => {
     cy.get(className).find('span[aria-label="close"]').click();
     cy.get(className).should('not.exist');
 });
+
+Cypress.Commands.add('movingTask', (taskName, projectName, labelMappingFrom, labelMappingTo, fromTask) => {
+    if (fromTask) {
+        cy.contains('.cvat-text-color', 'Actions').click();
+        cy.get('.ant-dropdown').not('.ant-dropdown-hidden').within(() => {
+            cy.contains('Move to project').click();
+        });
+    } else {
+        cy.contains('strong', taskName).parents('.cvat-tasks-list-item').find('.cvat-menu-icon').click();
+        cy.get('.ant-dropdown').not('.ant-dropdown-hidden').within(() => {
+            cy.contains('Move to project').click();
+        });
+    }
+    cy.get('.cvat-task-move-modal').find('.cvat-project-search-field').click();
+    cy.get('.ant-select-dropdown').not('.ant-select-dropdown-hidden').within(() => {
+        cy.get(`[title="${projectName}"]`).click();
+    });
+    if (labelMappingFrom !== labelMappingTo) {
+        cy.get('.cvat-move-task-label-mapper-item').within(() => {
+            cy.contains(labelMappingFrom).should('exist');
+            cy.get('.cvat-move-task-label-mapper-item-select').click();
+        });
+        cy.get('.ant-select-dropdown').not('.ant-select-dropdown-hidden').find(`[title="${labelMappingTo}"]`).click();
+    } else {
+        cy.get('.cvat-move-task-label-mapper-item').within(() => {
+            cy.get('.cvat-move-task-label-mapper-item-select').should('have.text', labelMappingFrom);
+        });
+    }
+    cy.get('.cvat-task-move-modal').within(() => {
+        cy.contains('button', 'OK').click();
+    })
+});