McCulloch will lead Rangers out against Elgin City this afternoon after accepting the captain's armband from McCoist.
And McCoist says the simplicity of the decision and McCulloch's reaction indicate just why he was the obvious choice.
The manager said: "I think the biggest compliment I can pay him is that it's just a natural, no brainer.
"He showed his loyalty to the club and his team mates by staying and putting in some very good performances this year in numerous positions.
"He leads by example and at this moment we see him as a perfect replacement skipper for Carlos.
"We know Carlos's strengths as a leader and a skipper and we see Lee in the same mould.
"The fact that it wasn't a decision we were pondering over for a long time would indicate just exactly what we think of Lee.
"He obviously accepted the role and he's as proud as punch."