There are two ways to add projects to a Team.
If you're in a Team, you can add your projects from the Team page itself using the Projects drop down, then checking "add to team page" next to projects you want to add
You can also add a project to a Team page from the Project Settings in the Project editor. To do this, go to Settings and click +Add Team next to "For a Team"
Then choose the Team(s) you'd like to add the project to. You don't have to be a member of a Team to add your project to the Team, but an admin will have to confirm that the project was created for their Team before it will appear.
Note: only public projects can be added to Teams