The 7-foot Miller averaged 8.8 points and 4.9 rebounds for Chicago last season. Miller played in Sacramento from 2003-09, including three seasons playing for current Houston coach Rick Adelman.
Agent Mark Bartelstein said in a phone interview on Saturday that reuniting with Adelman was a major factor in Miller's decision.
"Coach Adelman was a huge part of it," Bartelstein said. "He had a great time playing for him, and he thinks he's a great, great coach."
The 34-year-old Miller will back up All-Star center Yao Ming, who's expected to return healthy next season after sitting out a year to recover from foot surgery.
The Rockets initially pursued Chris Bosh when free agency opened on July 1, but Bosh chose to join LeBron James and Dwyane Wade in Miami. Houston agreed to terms this week with restricted free agents Kyle Lowry and Luis Scola.
Miller will enter his 13th NBA season. His best year came in 2003-04, his first with the Kings under Adelman, when he averaged 14.1 points, 10.3 rebounds and 4.3 assists per game. He averaged a career-high 15.6 points in 2004-05.
The Rockets were undersized last season and missed the playoffs with a 42-40 record. Yao is coming off reconstructive surgery on his left foot, and the team has said his minutes will be carefully monitored next season. Miller played in all 82 regular-season games for the Bulls last season, averaging 24 minutes per game.
Bartelstein said Miller was courted by several teams, but saw championship potential in Houston.
"The Rockets have a chance to be really good next year," Bartelstein said. "With Yao being back, they've also got a lot of really good pieces. They could really be a championship contender."