Bruce will earn £2million a year on his four-year contract while Whelan spent £3million in compensation to get him.
Whelan said: “What Steve earns he deserves. He will keep us out of relegation problems and all the fans will be delighted.
“We’ve got to do the right thing for Birmingham. David Sullivan has been a good and honest man all through the dealings.
“The important thing is we’ve got a brilliant manager and together we have to make Wigan what it once was — a fighting team.
“Under Steve Bruce we know we will be a team of fighters.
“I’m delighted we’ve got him, I think he’s a big loss for Birmingham and a big signing for Wigan Athletic.
“He’s one of the best young managers in the land. He’ll bring enthusiasm, knowledge and spirit to our team.
“We’ve had some bad luck with injuries and, when Steve comes in, I know he will want a midfield player and maybe a striker. I will be backing him exactly the same way I did with Paul Jewell.
“When Paul decided he was not going to come back I was a little bit disappointed — but Steve Bruce is the guy we wanted.”