The 26-year-old midfielder returns to the Premier League after signing a contract at Turf Moor that runs until 2020 with an option for an extra year.
Westwood made 161 appearances for Aston Villa, 124 of which came in the top flight, after joining from Crewe Alexandra in 2012.
“I’m delighted to be here. It’s happened fast but I’ve been made to feel very welcome and I can’t wait to get going,” Westwood told the club’s official website.
“It feels like a proper football club and homely and that’s what I like. I like to be appreciated and I think I will definitely get that here.
“The manager at Villa said I could speak to Burnley and for me that was perfect – a fresh start because things had got a bit stale at Villa. It’s a fresh start and I want to show people what I can really do.
“I have had some great times at Villa but recently it’s not been too good. I’m back in the Premier League and I’ve got another chance – coming here into a dressing room like this, full of British talent, and people who want to do well.
“I fit that bill and hopefully we can grow as a team and keep on improving.”
Burnley lost Dean Marney to a season-ending anterior cruciate ligament last week, and Westwood’s arrival provides manager Sean Dyche with additional depth in midfield.
He will not be available for Tuesday’s meeting with Leicester City but could feature against Watford on Saturday.