The school appealed to the NCAA after Cook's senior season ended with a knee injury. Cook played in 11 games before the injury Dec. 20 against Duke.
"Our hearts went out to Mike when he suffered the injury against Duke and we feel for him now," Pitt athletics director Steve Pederson said in a statement released by the university.
Under NCAA rules, an extra year of eligibility is possible if the athlete plays 30 percent or fewer of the team's games. Pitt played 37 games last season -- but that included six postseason games (four in the Big East and two in the NCAA tournaments), which under NCAA rules count only as one combined game for medical redshirt purposes.
That means Cook played in 34 percent of the Panthers' games.
"Situations like this are hard to take when you know how dedicated Mike's life has been to playing basketball," Pitt coach Jamie Dixon said in a statement released by the university. "Over the last three years, Mike has contributed significantly to our success both on and off the floor and has been an important member of our basketball family."
Last year, Cook played in Pitt's first 11 games before getting hurt. Junior point guard Levance Fields hit a game-winning 3-pointer in overtime and dedicated the win to Cook, his best friend. Two days later, Cook underwent surgery to correct a torn anterior cruciate ligament and medial and lateral meniscial tear.
Pitt was 40-8 with Cook in its starting lineup, Dixon said.
Cook started 48 consecutive games before getting hurt. Cook transferred from East Carolina after the 2004-05 season and sat out the 2005-06 season because of NCAA transfer rules. He graduated with a degree in communications last spring.
Pitt returns three starters, each of its top three scorers and seven of its top-10 letterwinners to a team that won the Big East tournament title, finished 27-10 overall and made its seventh consecutive NCAA tournament appearance.
Information from The Associated Press was used in this report.