Speaking about Barnett, who is expected to make his City debut against Derby County tomorrow night, Coleman said to the CT: "He's 6ft 1in, strong and very athletic and we are delighted to have him here.
"Leon has lacked a bit of football because of a knee injury but I am not worried about his fitness because he did a full pre-season and came through 90 minutes in the reserves this week when he did everything we expected him to do.
"He has got a lot of experience in this league and played a big part in West Brom's promotion campaign two years ago, but we are not expecting miracles from him against Derby.
"I have seen him a lot and he is the right age and I believe he will do a very good job for us over the next three months.
"I have made no secret of the fact that I have been looking to strengthen at the back but we wanted to make sure we got the right man in."