Miller attracted interest from numerous other teams but was strongly lobbied to move to Houston by Rockets coach Rick Adelman, who coached him in Sacramento, and guard Kevin Martin, who was Miller's teammate on the Kings.
Miller said the opportunity was "too good of a deal to pass up," according to the Chicago Tribune.
"It's my favorite coach [Adelman] I've ever played for. I know [Martin] real well from our Sacramento days. Luis [Scola] had a heck of a year. And I finally get to play with Yao [Ming] instead of guarding his big butt. The team is pretty solid," he said, according to the report.
The third year of the contract is partially guaranteed, sources said.
His agent, Mark Bartelstein, confirmed the deal, according to KRIV-TV in Houston.
"Brad is really excited. The prospect of Yao being back coupled with the fact he will be playing for Rick Adelman makes Houston a special place," Bartelstein said, according to the report. "He has a great relationship with Rick."
Amid its well-chronicled interest in trying to pursue Chris Bosh in free agency, Houston also targeted Miller early as an ideal complement to Yao and Scola and as a player who could help facilitate Adelman's offense.
Miller, 34, made two All-Star Games as a member of the Kings and spent the past season and a half with the Chicago Bulls. It was the second stint in Chicago for Miller, who has also played in Charlotte and Indiana.
Atlanta, Boston, Miami and Cleveland are among the teams that courted Miller since free agency began July 1, with Chicago also expressing interest in re-signing him.
Bulls forward Joakim Noah was sad to hear the news that his veteran mentor was on his way to Texas.
"I learned a lot from Brad," Noah said in a text message to ESPNChicago.com. "It's going to be very different with him not around. He's a real professional."
The pair struck up a bond after Miller was traded back to the Bulls in the middle of the 2008-09 season. They could usually be seen joking around about something in the Bulls locker room and Noah consistently referred to his buddy as "The Duck". The Bulls had hoped Miller returned to continue to serve as a backup center/mentor to Noah.
"I wish him nothing but the best," Noah continued. "We're going to miss the bash brothers."
Marc Stein is a senior NBA writer for ESPN.com. ESPNChicago.com's Nick Friedell contributed to this report.