Sunderland accepted a bid from Palace on Friday after Van Aanholt submitted a transfer request, opening the way for the 26-year-old to be reunited with Sam Allardyce, having previously worked with the manager at the Stadium of Light.
"Finally got Patrick over the line. You like to bring players you've worked with before and should bring something to the team," Allardyce told reporters on Monday.
"Hopefully his impact is instant. He was instrumental in Sunderland's fight for survival last year, not just as a full back but for goals," Allardyce added of the full back who scored eight times in 95 appearances for Sunderland.
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"We want him to defend well because we're conceding too many goals. He'll help at both ends."
Palace are 18th in the league on 16 points after 22 games and travel to 12th-placed Bournemouth on Tuesday. Sunderland, who are bottom on 15 points, host third-placed Tottenham Hotspur at the same time.
(Reporting by Shravanth Vijayakumar in Bengaluru)
