The former Hoops boss was unveiled as the new Scotland boss this week and his former pupil Brown believes he is easily the best man for the job.
"I'm delighted - it's a great move for Scotland," said Brown.
"To be fair, it was about time they named a manager, and as far as I'm concerned they couldn't have picked anyone better. We have all been hoping it would be him.
"The bookies made him favourite and at that point I spoke to a few of the lads who played under him and we all agreed, it would be great if he was actually appointed.
"They took their time but at the end of the day they got the right man for the job, which is the main thing."
He added: "He did a lot for my career.
"He signed me (from Hibernian in 2007) and showed a lot of faith in me.
"He's a great man-manager who knows how to handle big-time players as well as players coming through.
"He's a good man to have in charge."