Dohmann, a 32-year-old right-handed pitcher, pitched for Hiroshima in Japan last year, until he was released. He returned to the United States and pitched briefly for Arizona's Triple-A affiliate in Reno, going 0-1 with a 6.14 ERA.
Green is coming off back disk surgery and will have a chance to replace departed free agent Juan Castro as backup to starting shortstop Rafael Furcal. The 32-year-old Green played for Boston in 2009, batting .236 with six homers and 35 RBIs in 103 games. He's also played for the Mariners, Yankees, Blue Jays and Braves.
Reyes, a 28-year-old middle infielder, played nine games for the Mets last year.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.