(In order to archive tasks, you need to be a premium member.)

Mobile:

Option 1: Long-press (Android) or left-swipe (iOS) the task. A menu will pop up, giving you a choice to archive that task.

Option 2: In settings menu, choose the option ‘Archive Completed Tasks’

Web:

Option 1: Hover over the task, an Archive icon will be shown. Click it.

Option 2:  In settings menu, choose the option ‘Archive Completed Tasks’