Yahoo! Sports' Adrian Wojnarowski reports the deal will send Brewer and Turiaf to Houston for guard Troy Daniels.
The trade also includes a pair of second round draft picks.
Turiaf was then traded to Philadelphia.
Turiaf underwent arthroscopic surgery on his right hip this week and will miss the remainder of the season.
Rumors of Brewer being back on the market began to rumble again this week, after Wolves President of Basketball Operations Flip Saunders pulled him off the trade block last month.
The Rockets used their trade exception from the deal that sent Jeremy Lin to Los Angeles, to acquire Brewer.
Brewer is averaging 10.5 points, 3.3 assists and 3.9 rebounds per game for the Wolves this season.
"Kind of mixed emotions just because I really love Minnesota," Brewer told the Star Tribune. "People don't understand how much I love Minnesota. I wanted to end my career here. That's why I signed back here. I thought it'd be possible, but I understand we're going young. It's going to be a few years, but the Wolves have great, young talent."
The deal with Houston reunites him with former Wolves executive Kevin McHale, who now coaches the Rockets. McHale originally drafted Brewer when he was with the Timberwolves.
According to Wojnarowski, Houston was interested in Brewer for his ability to defend at the small forward position. He will play behind Trevor Ariza.