The New Jersey-born midfielder will play for Villa until the end of the season when the move could be made permanent.
Irish midfielder Stephen Ireland will not be playing alongside Bradley, however, after he was loaned to Newcastle United following a disappointing spell at Villa since signing from Manchester City.
The 23-year-old Bradley, son of U.S. coach Bob, has won 50 caps for his country after making his name with New York MetroStars and Dutch club Heerenveen.
"For me the Premier League is the best league in the world," Bradley told Villa's website. "The speed of the game, the pace and the power all stand out.
"I heard that (manager) Gerard Houllier was interested in bringing me here. From that moment I was excited and just hoping that everything could get done."
Bradley will have to wait for international clearance before making his Villa debut.
Fellow American Clint Dempsey has enjoyed a successful spell at Fulham and Landon Donovan impressed during a short loan period at Everton. Midfielder Stuart Holden is at Bolton Wanderers while Jonathan Spector plays for West Ham United.
Bradley will have fellow countrymen for company at Villa in the form of goalkeeper Brad Friedel and defender Eric Lichaj.
