Palace's official website (www.cpfc.co.uk) said his contract was for five years.
Wickham, 22, had his best period at Sunderland at the end of the 2013-14 season, when a flurry of five goals in three games lifted them from the bottom of the Premier League to 17th place and eventual safety.
Those were his only goals from 15 appearances and last season he managed a modest five in 36 games.
His total for the club was 15 in 91 matches in all competitions.
"I looked at the team before I arrived here and the signings that have been brought in, and the potential to score goals and the chances that could be created was a massive influence," Wickham told the club website.
Manager Alan Pardew has been keen to strengthen Palace's attacking options in an attempt to build on last season's 10th position, after they had been in danger of relegation when he joined in January.
Palace have also signed Patrick Bamford, the promising young Chelsea forward, on loan.
(Reporting by Steve Tongue; editing by Martyn Herman)
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