Greene, 28, was scheduled to arrive in Houston on Thursday night and be in uniform for Friday's series opener against the Brewers at Minute Maid Park. The Astros will make a corresponding roster move in time for Friday's game.
Astros general manager Jeff Luhnow was the Cardinals' scouting director when the club drafted Greene out of Georgia Tech with the 30th overall pick in 2005.
"He's got all the talent in the world to be a successful Major League player," Luhnow said. "He's shown flashes of having success in St. Louis. Obviously, he was part of the world championship team last year. He can run. He can hit. He can hit for power. He can field. He can throw. Hopefully he'll feel like he's got an opportunity here to do that in a little bit more relaxed atmosphere and show us what he's capable of doing."
Greene didn't live up to his potential in St. Louis, hitting .218 in 227 games. He's appeared in 77 games this year, including 40 starts at second base and four at shortstop. The right-handed-hitting infielder has appeared at every defensive position other than catcher and pitcher in his career.
"I'm excited to be down there and to contribute and to play," Greene said. "What's happened here in the past stays here. This is a new start for me with Houston. I'm excited about that."
Greene and Gonzalez, a switch-hitter, will split time at shortstop. Gonzalez, a Rule 5 Draft pickup, has gotten most of the time at shortstop since Lowrie went down. Brett Wallace and Matt Downs are capable of playing shortstop, but they are both better suited on the corners.
"When your backup at shortstop is Brett Wallace, you've got to think of other options," Luhnow said. "Brett's done a terrific job of being in that role [he played 10 games at shortstop in Triple-A], but every time Marwin goes out there and looks like he's possibly going to be involved in a play that might cause an injury, we all get nervous. It's going to be nice to have two shortstops. Tyler's ready to take the challenge on. I'm looking forward to it."
Discussions between the Cardinals and Astros went on for a few days before the trade was completed, after the Astros had claimed Greene off waivers.
"It's kind of bittersweet," Greene said. "I came up with this organization, lived and breathed with these guys for a long time. It's sad in the sense that these guys are my friends and my family and we've all grown up together. I've been nothing but thankful and grateful to the organization for giving me the opportunity and to have faith in me and stay confident with me through the years."
To make room on the 40-man roster for Greene, the Astros designated Triple-A infielder Brian Bixler for assignment.