The 26-year old defender heads to the 2012 MLS Cup runners-up in exchange for allocation money after spending two seasons in Portland and Dynamo boss Dom Kinnear was happy to add his to the roster.
"I think Eric is a good center back," said Kinnear.
"He is both good in the air and with the ball at his feet. He has good pace and is also good on set pieces. He has done well in the past with Portland and Columbus (Crew).
"I think he is going to be an important part of the team next year, with the amount of games we're playing and tournaments we're in, and the possibility of losing players to the Gold Cup."
Brunner, who has made 84 MLS appearances for both the Crew and the Timbers, was looking forward to a new challenge in Houston.
"I am definitely excited to join the Dynamo," said Brunner. "There is a lot of history in Houston, and it is an honor and a privilege to join a team that has made the MLS Cup the last two years. I am definitely excited to be included in that rich history."