Australia international midfielder Skoko, 32, made 53 appearances, including 45 in the Barclays Premier League, after joining Wigan in August 2005 from Turkish side Genclerbirligi on a three-year deal.
"It's always sad saying goodbye to good pros," said Bruce.
He added: "Josip is a quality player who has never given me one bit of trouble, has always given me everything when selected and we wish him all the best."
Bruce has offered Skoko the opportunity of training with Wigan in pre-season to maintain his fitness should he not immediately find another club.
Cameroon midfielder Olembe figured in only nine games this season, starting on three occasions, after signing a one-year deal last summer.
"Again, I have no complaints about Salomon, who has always trained professionally and given me everything when called upon," remarked Bruce about the 27-year-old.
Young professionals Peter Moore and Russell Saunders, neither of whom made a first-team appearance, have also been released after the expiry of their contracts.