The Detroit Free Press was the first to report the deal, which includes an invitation to Spring Training, and MLB.com has also confirmed the news.
"There were [talks with the Tigers]," Kelly said. "[It] wasn't an easy decision, but Miami was a better fit at this time."
Kelly, 34, spent the past six seasons with the Tigers and played at least 95 games in four of those years.
Kelly played first, third and outfield as a member of the Tigers last season and hit .245.
William Boor is a reporter for MLB.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.