Adeiny Hechavarria, acquired from the Blue Jays in November, is projected to start at shortstop, and Donovan Solano is the front-runner to win the second-base job. Those are the only two on the 40-man roster who are accustomed to shortstop.
Green can play shortstop, second base and third base.
Green enters Spring Training in a similar situation as a year ago, when he initially signed a Minor League deal with Miami with an invitation to camp.
In 2012, Green spent most of the season with Triple-A New Orleans, batting .344 in 63 games.
With the Marlins, Green appeared in seven games before his season was cut short by a left thumb injury suffered on Aug. 12. He is now fully healthy.
Green broke in with the Braves in 2004, and he has played in parts of seven big league seasons.
Adding Green comes a few days after Miami agreed to terms with Austin Kearns on a Minor League deal with an invite to Spring Training.
Kearns was a right-handed pinch-hit option for the Marlins last year.
Also on Tuesday, the Marlins signed right-hander Michael Wuertz to a Minor League deal with an invitation to Spring Training, according to a tweet by the Beverly Hills Sports Council.
Wuertz, 34, last pitched in the big leagues in 2011 with the A's, appearing in 39 games of relief. The right-hander broke in with the Cubs in 2004, and he has appeared in 426 games in eight seasons.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.