The 30-year-old has reportedly signed a three-year deal with a net of €1.75 million per season until the summer of 2024 with the Istanbul-based club.
Van Aanholt, joining Palace in 2017 made a total of 134 Palace appearances, scoring 14 times.
The full-back was among the Netherlands national team squad at Euro 2020 this summer as he made four appearances for the The Flying Dutchmen.
Van Aanholt’s saw his contract with Crystal Palace ran out earlier in the summer as that attracted interest from several clubs in signing him as a free agent.
Inter Milan was speculated to be his next destination but Aanholt has moved to Turkey instead.
The 30-year-old has penned a three-year deal with the Yellow-Reds after undergoing his medical.
Crystal Palace are in the hunt for a perfect replacement for the defender as the new season is set to begin.
Galatasaray will face Scottish side St Johnstone in the Europa League on August 5 in Turkey, a game expected to be played behind closed doors.
Van Aanholt after putting pen-to-paper wrote on his twitter account to show appreciation to Palace for the time spent with the club.
He tweeted: "So many words, what to say. Thank you for the 4.5 years. Palace has been a proper home to me, you'll forever be apart of my life. To the boys, good luck for the up coming season. Big change big opportunity big rewards. Make it count."
Crystal Palace on their official website added;
"Everyone at Crystal Palace wishes Patrick the very best for the future, and thanks him for his service."
