The Norwegian striker had medicals at both the Britannia Stadium and the Hawthorns this week, but the 31-year-old has decided to join the Potters ahead of the Baggies.
Carew is due to run out of contract at the end of the season and his move to Stoke could become a permanent one in the summer if he does enough to earn a contract during his loan.
The big forward has fallen out-of-favour at Villa since the arrival of Gerard Houllier - with Darren Bent's arrival pushing him further down the pecking order.
The striker called Houllier "disrespectful" after he was challenged to earn a new contract, with the war of words continued by the Villa boss, who told Carew to stop "living in the past".
His arrival at Stoke could well hasten the departure of Ricardo Fuller, who looks set to leave the Potteries after Stoke accepted a £3m bid for the forward from Sunderland.
Carew will compete with the likes of Kenwyne Jones, Jonathan Walters and Tuncay for a place in the starting XI, while Mamady Sidibe could return from an Achilles injury next month to further boost boss Tony Pulis' options in attack.