Yes, applications can be transferred. The app key will stay the same, so you do not need to make any changes to your application.
To transfer an application to a different team:
Open the application you want to transfer
Go to the Settings tab
Change the team where the application belongs
To transfer a team to someone else:
In the sidebar, click on the Team Settings (cog) icon
Add the new person to the team, if not there already. If you just added the person to the team, they will need to accept the invitation.
Change the permissions of the person to Owner.
Optionally, leave the team by pressing the X icon next to your name.