The Latics will pay Bruce's former club Birmingham £3million as compensation after the 46-year-old manager terminated his contract with Blues.
"£3million is a spot on figure. Steve is one of the best young managers in the land, along with Mark Hughes. Sir Alex Ferguson will always tell you those two boys are quality," Whelan told Sky Sports.
After failing in his attempt to lure Paul Jewell, with whom Wigan secured Premiership safety last season, Whelan turned his attention to Bruce.
"When Jewell decided he wasn't going to come back I was a little disappointed, but I've had Bruce before at Wigan and Steve Bruce is the guy we've wanted," he said.
"From the very outset he was the one to replace Paul Jewell, so I'm delighted we've got him. It's a big loss for Birmingham and a terrific signing for Wigan Athletic."
Bruce, who had a brief spell with Wigan in 2001, have an uphill task ahead of him as the club lie second from bottom in the Premiership table on eight points.