The midfielder - a product of the successful academy at Crewe, making his debut against Millwall aged 18 - is Lambert's seventh signing of the summer.
He was part of the side that clinched promotion to League One after defeating Cheltenham in the play-off final at Wembley last season, making over 100 appearances for the Railwaymen and the Villa boss has no doubt that Westwood has the qualities to make an impact.
"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," Lambert told Villa's website.
"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."