The young midfielder played a pivotal role as the Railwaymen sealed promotion from League Two last season, but will now ply his trade in the top flight at Villa Park
The 22-year-old midfielder, who can also operate in defence, was delighted to make the move and likened himself to Manchester United's England international, Michael Carrick.
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Westwood told the club's official website: "I see myself as a Michael Carrick-type of player, someone who stays out of the limelight and keeps it simple, retaining the ball and laying it off to team-mates and from the conversations I've had with the new manager I think that will fit in perfectly here.
"This is a fantastic football club, a massive club and I can't wait to get started really.
The midfielder, who came through the ranks at Gresty Road, making his debut at the age of 18 against Milwall, is the seventh addition made by manager Paul Lambert this summer.
Westwood made over 100 appearances for the Railwaymen and his new boss is confident the youngester will be a hit at Villa Park.
Lambert added: "Being captain of his football club at 21 years of age, I think that says a big thing about Ashley's quality, the responsibility he has taken on his shoulders and his temperament - he's a good player.
"He's also a terrific prospect for this football club - a real, real talent.
"He's had a really good grounding at Crewe and he will fit in with what we're looking to do here. He's a good player and he'll do fine."