Bruce was finally confirmed as Black Cats boss on Wednesday afternoon when the Wearsiders agreed a suitable compensation package with the Latics following two days of negotiations.
He will be joined at the Stadium of Light by assistant Eric Black, goalkeeping coach Nigel Spink and reserve team boss Keith Bertschin.
"Everyone associated with Wigan is devastated that Steve and Eric have gone, we would be lying if we said any different," said Whelan.
"But things can change very quickly and I have always said I would not stand in anyone's way who wishes to leave the club, as long as the terms are in the best interest of Wigan.
"What Steve has achieved here over the past 18 months has been magnificent. After a period of instability, he put the team in order and started laying the foundations for a prosperous future. We finished in our second-highest ever league position this season and this is something we will be looking to build upon going forward."