Signed on loan a month ago, Carew has scored twice in City's last three matches, with the Norwegian netting the opener in Saturday's 3-0 FA Cup fifth-round victory at home to Brighton.
"Everything is going fantastically for me personally, and for the football club," Carew told the club's official website.
"I feel at home here, the supporters have been fantastic with me and all of the players, management and everyone else at the club have made me feel unbelievably welcome."
Source: PA
Source: PA