The 25-year-old winger made 168 appearances and scored 19 goals in seven seasons with Hearts, and appeared 28 times this season, scoring twice.
“Andrew is good at taking people on, he crosses a good ball and can take set pieces,” said Dynamo head coach Dominic Kinnear in a team statement. “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 represented England at the 2009 U-21 European Championships but is eligible to represent Scotland at the international level as well.