The User Story can be archived once it’s status is completed. To Archive the User Story in Kanban Board from its Task View,

1. Move all the task(s) from a Story to the Completed lane there you can view Archive this story tag.

To Archive the User Story in Kanban Board from its Story View,

1. Move the User Story to the Completed lane directly from there you can view Archive this story tag.

Once you click on Archive this story tag, all your archived user stories will be moved to Archived User Stories section.