"I am extremely confident he will do well at Tottenham," said the former Scotland boss.
Hutton has completed a startling transformation in the 12 months since Smith returned to Ibrox, but the Rangers boss is refusing to take any credit for the talented defender's development.
"You have to give him all the credit for his performances," Smith insists.
"I didn't go out of my way to do anything special with him. His level of performance has been excellent and he now has the confidence to go along with that.
"Everybody at the club, from the chairman down, is disappointed from a football perspective that he's leaving.
"But we all know the reality of the situation is that it's the type of offer we couldn't turn down."