Board Thread:Questions and Answers Forum/@comment-28170719-20160424053820/@comment-25916964-20160424112435

On Xbox One hold the Xbox button when the notification is visible, or go to the Xbox Guide by double tapping the Xbox button, then navigate to the notifications section where you can select the invite.

I'm unfamiliar with Xbox 360, but opening the Xbox Guide by tapping the Xbox button, navigating to messages and selecting the invite should do the trick. Holding the Xbox button when the notification is visible may also apply to Xbox 360.

As for PlayStation consoles? I haven't a clue.