When a task assigned to you is in your Inbox, and you complete it, the task remains in your Inbox. It is one more item you have to clear from your Inbox.
If a task is assigned to the person that completes the task, have an option to remove these items from the Inbox.
Example,
Task was in the section “Past 7 days”
Task is due tomorrow
I completed the task today
Task was marked as completed in the Inbox
I still needed to archive the Inbox item
Welcome to the Forum @Ryan_Sunderman and thank you for sharing your feedback with us!
There is an existing thread regarding this topic so I’ve gone ahead and merged your post with it for consolidation purposes. Please don’t forget to cast your vote! 
Thank you again for taking time to share your feedback! Have a nice day!
Hi, I found that at the end of the list of archived tasks, there is an option to archive all messages
Instead of archiving notifications about completed tasks, it should be possible to manage this on project level. As it is, you can choose to get notifications about tasks addes, comments and status updates. Why not add the option if you want to be notified about completed tasks.
I experience the same inbox problem, i.e. getting cluttered with notifications of tasks that are completed by others. I own and manage the project they work in, so there is no escaping the useless notifications.
I agree - this should be a setting at the project level. Hoping Asana will be able to come up with a solution for this sooner rather than later.
Hi,
Just following up on this.
We’ve set-up automations on projects that change assignees and due dates based on things being completed (partially using Flowsana).
But, this seems to be causing a lot of notifications to be sent on tasks that are already completed (the due date has changed, the assignee has changed, etc.).
Would love for an option to be able to turn off certain notifications on completed tasks so that people aren’t peppered by these kinds of things.
Adding support to this request… I can’t imagine a scenario in which someone would want to see completed tasks in their inbox. I try to keep my inbox as an immediate to-do list, and spending half the time clearing already completed tasks feels like a huge waste of time.
At least give the option to hide completed tasks. The filter is already there, it just needs a “Hide completed tasks” view 
What is happening with this request? What our employer is paying for us to clear out other team members completed task from our projects is such a waste of time and money for the employer. It is logical that there is already a dropdown - let there also be the choice to “hide” at least - completed tasks on each project, or as a whole within the inbox.
I agree with this entire thread! The inbox is awesome EXCEPT I don’t use it because the completed task notifications are redundant to clear nad they take SOO much time to clear. I also lose ACTUAL notifications in teh Asana inbox because there’s so many completed task notifications to sift through.
The idea to add one filter to the existing filter list, so you can toggle it on or off if you want Completed Task notifications or not is great! OR the idea to have a “archive all completed tasks” notifications. Either, or both. But it’s been sine 2018 that people have requested this… PLEASE implement! Our team can’t use the Asana inbox effectively until this feature is created.