The Dutchman had emerged as the favourite to replace Sam Allardyce as head coach of Palace over the last week, and the 112-time Netherlands international has now signed a three-year deal at Selhurst Park.
The 47-year-old took control of Inter Milan last summer, but he lasted just three months with the Italian giants, losing seven of his 14 matches in charge.
De Boer won five Dutch league titles as a player during his time at Ajax, before leading the club to four league titles as manager between 2010 and 2016.
Palace chairman Steve Parish told the club’s official website: “We have undertaken a thorough interview process to ensure we are in a position to appoint a manager of the calibre and experience that Frank brings with him.
“I am pleased to welcome him to Crystal Palace and I know he cannot wait to get started and prepare for our record breaking fifth season in the top flight.”
Meanwhile, De Boer added: “I am thrilled to be appointed as manager of Crystal Palace football club. It is a great honour to take charge of such an historic club, a club that is known around the world for its hugely proud and passionate fan base.
“This role is a hugely exciting opportunity for me, and I cannot wait to get started in the Premier League with the players and staff here in South London.”