The 27-year-old's stay with the fourth-placed Canaries will include any potential Championship play-off games.
Dorrans has played eight times since joining the Canaries on an initial one-month deal in February.
"He's got a football brain, he can get about the pitch, he's physically strong and can carry out a variety of roles within the team," said boss Alex Neil.
"He's very versatile, which is ideal for a manager."
Norwich City have extended the loan of West Bromwich Albion midfielder Graham Dorrans until the end of the season.