The Potters made their move for the 31-year-old, who is out of contract in the summer, after Darren Bent's £24million arrival at Villa Park pushed the Norway international further down the pecking order.
Loan star: Carew has traded Villa Park for the Britannia Stadium
Carew completed his medical on Thursday and finalised the paperworkthis morning in time to be included in the squad for Saturday'sBarclays Premier League trip to Fulham.
And the striker believes a successful four months at the Britannia Stadium could lead to a permanent deal.
'If I'm happy and the club is happy, if I enjoy it and it goes well enough, then we can decide that in the summer,' Carew said.
Off colour: Carew has failed to score a single goal for Villa this season
'The important thing now is to make the most of this opportunity.'I'm looking forward to the challenge and I am happy to be here.
'Although I had other offers, I saw Stoke as the best team and thestrongest team, so this is a great chance for me to join a sidefighting in the top half of the table.
'Tony Pulis has shown great confidence in getting me here so I want to repay that faith.'
'This is a fantastic signing,' manager Tony Pulis told the club's website. 'John's record speaks for itself because he has scored goals at the highest level throughout his career.
'As well as the experience he has gained at international level he has played for some top clubs across Europe and performed in the Champions League for many seasons, including an appearance in the final for Valencia.
'On top of that he was Aston Villa's leading scorer last season with 17 goals so we have acquired a striker with an outstanding pedigree.'
Carew set to snub West Bromwich to join Stoke on loan from Aston VillaSunderland ready to land £3m-rated Stoke striker Fuller to replace BentAll the latest Stoke news, features and opinionAll the latest Aston Villa news, features and opinion
Explore more:People: John Carew, Tony Pulis, Darren Bent Places: Norway, Europe