Norris signed with the Sugar Land Skeeters of the Atlantic League on Monday, Chris Cotillo of SB Nation reports.
Norris or Brayan Pena could make the Tigers' Opening Day roster as a third catcher, behind starter James McCann and John Hicks, Jason Beck of MLB.com reports.
Norris signed a minor-league contract with the Tigers on Tuesday which includes an invite to spring training.
Norris was suspended for the rest of the 2017 season following a domestic violence investigation, Jorge Castillo of The Washington Post reports.
Norris was released by the Rays on Tuesday, Marc Topkin of the Tampa Bay Times reports.
Norris will be designated for assignment Saturday to clear space for Wilson Ramos's return from the disabled list.
Norris went 3-for-3 with a two-run homer and three runs Friday against the Orioles.
Norris is out of the lineup Wednesday against the Reds, Bill Chastain of MLB.com reports.
Norris is not in the lineup Tuesday against the Reds, Marc Topkin of the Tampa Bay Times reports.
Norris went 1-for-4 with a solo home run in Sunday's 9-1 win over the Tigers.