Wojcik replaces the retiring Bobby Cremins, who was replaced by interim coach Mark Byington when Cremins had to take a leave of absence during the season after 11 games.
Wojcik will receive a five-year contract. A news conference is scheduled for Wednesday.
Wojcik was fired earlier this month after he led the Golden Hurricane to a 17-14 record, 10-6 in Conference USA.
Wojcik was the head coach at Tulsa for seven seasons and had a winning record in each year except his first. He won 20-plus games in four of the seven seasons and finished with a 140-92 record, 68-44 in Conference USA.
Wojcik led Tulsa to three postseason appearances, including two NIT berths, but never an NCAA tournament appearance.
Wojcik has coached at his alma mater Navy, Notre Dame, North Carolina and Michigan State.
Charleston finished the season with a 19-12 record, 10-8 in the Southern Conference.
Cremins coached Charleston for six seasons and led it to three postseason appearances, including the NIT quarterfinals. The Cougars never made the NCAA tournament under Cremins, who came out of retirement to replace Tom Herrion in 2006. Cremins retired at Georgia Tech in 2000.