The forward was handed the armband by manager Ally McCoist for the weekend victory over Elgin as he replaced Carlos Bocanegra following his departure for racing Santander.
Although it is only now McCulloch is recognised as the team’s leader, he has shown all the qualities required to do that ever since Gers went into administration in February.
And Hateley has continually been impressed by the way the 34-year-old has kept demonstrating the right attitude for the Ibrox side.
McCulloch has enjoyed a lot of success since moving up front and after five goals at the tail end of last term, he has eight to his credit so far this season.
Hateley, speaking tonight on RangersTV.tv, said: “A shining example of people who have come forward during all the troubles we have had is Lee McCulloch.
“You will see a lot of him in the team this year. He’s a guy who can play all over the place and you never lose that knack of scoring that he has.
“It’s a great habit to have and that’s something Alistair will want all his strikers to have because when you score often, you move up the leagues pretty quickly.
“Lee is a smart lad, a decent player and he is playing for the club for all the right reasons. It’s easy to say he’s here because he’s at the end of his career.
“But money’s not everything for him now and he’s doing the right thing and playing for a football club where he is appreciated by everybody around him.
“The players, his colleagues, the fans and everybody associated with Rangers Football Club are pleased with him and I take my hat off to him. He has done a terrific job.”