The 25-year old winger departed Edinburgh earlier this week to finalise his contract with the Dynamo which has now been confirmed by the Texan club.
"Andrew is good at taking people on, he crosses a good ball and can take set pieces," said Dynamo head coach Dominic Kinnear.
"He is a hard-working player and I think he will definitely fit in with the team. He has a good attitude on the field and is versatile. He can play on the left or right side of midfield."
Driver spent seven seasons with Hearts, making close to 170 appearances, and joins the Dynamo on loan for the 2013 MLS season with his contract at Tynecastle Stadium set to expire in June.
He was thrilled to embark on a new chapter in Houston: "I am very excited about the opportunity to come and play for the Dynamo.
"I have followed MLS over the years and Houston has stood out as one of the top teams. I know a lot of success has been because of the work of Dominic Kinnear, so I am delighted to have the chance to learn from him and improve as a player under him."