Gibson, 28, who is an unsigned free-agent right fielder, married JoAnn Sklarski. Rozema, 29, who played with Gibson on the Tigers from 1979 through 1984 before joining the Rangers last season, married Sandy Sklarski. The Sklarski sisters are from Mount Clemens.
The double ceremony at Grosse Pointe Memorial Church began at 4:30 p.m. amid tight security aimed at allowing only the 600 invited guests, and no media, inside.
A reception followed at the Detroit Yacht Club on Belle Isle, and the couples were planning to depart Thursday for a honeymoon in Australia.