The deal will include a team option for next season.
Brooks had to clear waivers before becoming a free agent, allowing him to sign with any team.
He spent the first five seasons of his career with the Rockets, and was selected 27th overall by them in the 2007 draft. He had a superb year in 2009-2010 in Houston when he averaged 19.6 points per game, but has not come close to replicating that success in recent years.
Brooks saw a decrease in playing time with Isaiah Thomas and Jimmer Fredette getting the most action at guard. He is making $3.25 million this year, with a $3.44 million player option for next season.
In 46 games this season, Brooks is averaging 8.0 points per game.