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The Dutch international joined the English club for $17.4 million and could debut with his new team in Tuesday's English Premier League (EPL) game against Bournemouth, reports Efe.
According to Crystal Palace's website, coach Sam Allardyce said: "I am delighted that Patrick has joined us."
"We had great success together at Sunderland where he was instrumental in keeping them in the Premier League last season," the English coach recalled.
Allardyce said Van Aanholt will bring pace and energy to the London side through his strong defensive qualities and the ability to create and score goals.
The Dutch player appeared in 95 games with Sunderland since his move from Chelsea in summer 2014 for $1.8 million.
Crystal Palace's Tweeted to confirm the news. His tweet read:
Van Aanholt started his career at Chelsea, but spent his time on loan to Coventry City, Newcastle United, Leicester City, Wigan Athletic and Vitesse Arnhem.