The 19-year-old striker scored eight goals in 22 MLS appearances for the Fire last season and has three international caps to his name.
He becomes manager Unai Emery's second signing of the January transfer window following the arrival of full-back Alex Moreno from Real Betis.
A club statement read: "Aston Villa is delighted to confirm Jhon Duran has completed a permanent transfer from Chicago Fire for an undisclosed fee."
Duran is hoping to make his mark at the club quickly. He told Villa TV: "I have all the desire in the world. Lots of desire to work hard, give everything to the team and win. I'm hoping I can play soon.
"I'm a player that plays with a lot of passion who is dedicated to the team and a player that really wants to win always.
"I know it's the most important league in the world. It's the best league in the world, and I have all the desire in the world to get on the pitch and score that first goal."