"Carr has done well. His hunger has been superb ever since he arrived - he is a fully motivated player with the kind of quality that counts in the Premier League," Blues boss Alex McLeish told the clubs official website.
"He is always positive and says the right things - he has got a winner's attitude.
"Right-back was a problem position for us the whole of last season due to injuries. Nicky Hunt came in on loan and did a good job for us but then Bolton recalled him.
"But Carr came in and nailed the position. He's vastly experienced and in the crucial closing stages of our quest for Premier League status that experience told."