Rodgers, the Astros' third-round pick, and his family came to Minute Maid Park on Wednesday afternoon to sign the deal. Terms were not disclosed. The slot value of the 96th pick is $495,200.
"We're delighted to have him on board," general manager Jeff Luhnow said. "He'll be out playing in an Astros uniform really soon."
Rodgers stopped in Luhnow's office for a few minutes on his tour of Minute Maid.
"This is my future office, I'm hoping," Rodgers said.
Rodgers, who graduated from Lamar Consolidated High School in Rosenberg, Texas, in 2009, said his decision to sign was pretty easy.
"I knew what I wanted to do," Rodgers said. "With the Astros drafting me, it was pretty easy. The hometown team, the team I grew up loving. It's pretty simple. It was either sign or sign."
Houston will send Rodgers to Kissimmee, Fla., for a few weeks to work out at the Astros' Spring Training site. He will then be sent to Tri-City, the Class A short-season affiliate of the Astros, in the New York-Penn League.
Having his next few weeks set up was definitely comforting to Rodgers.
"Now I got that weight off my shoulders, and now I can just focus on becoming an Astro and playing at Minute Maid and playing with these guys out there," Rodgers said.
Rodgers was drafted out of high school in the 39th round by the Milwaukee Brewers in 2009, but opted to go to Arizona State.
In his final season at Arizona State, Rodgers had a 2.11 ERA and walked just 11 batters in 72 2/3 innings. He has a 90-92 mph fastball and three secondary pitches -- a slider, a curveball and a changeup.
Assistant general manager/scouting director Bobby Heck said the Astros liked Rodgers' success in the Pac-12 and his command of his pitches.
"Anybody can throw a ball," Rodgers said. "It takes the good ones to be able to command all pitches. I'm still working on that."
Clark Goble is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.