"I had a blast playing for the Tigers, and it didn't end how I wanted it to, but it's part of this business and I'm on to the next chapter in my baseball career," Grossman said.
Detroit received Kris Anglin, a pitcher in Atlanta's minor league system, in exchange for Grossman, who has played both corner outfield spots for Detroit this season.
Relief pitcher Will Smith would go to Houston in the deal for Odorizzi, 32, who started on Sunday during the Astros' 3-2 victory over the Seattle Mariners. The veteran allowed two hits and struck out a season-high eight in seven scoreless innings versus Seattle, and he didn't yield a hit until the fourth inning.
To make room on the roster for Grossman, Atlanta optioned infielder Mike Ford to its Triple-A affiliate in Gwinnett, Georgia.
Information from The Associated Press was used in this report.