It marks De Boer's first managerial position since his ill-fated 85 days in charge of Inter, which came to an end last November.
De Boer previously trained Ajax for five seasons, when he won four Eredivisie titles.
The 47-year-old - who guided Ajax to four successive league titles before a disappointing short spell at Serie A giants Inter Milan - signed a three year contract.
"I have my own type of coaching and style of playing, but the most important thing is that I want us to play dominant [football] when we can", said the Dutchman.
Voetbal International have reported Frank de Boer will install Orlando Trustfull as his right hand man at Crystal Palace.
He said: "I've got my trust in Frank".
The Dutchman spent six seasons managing the Amsterdam club until leaving for Inter Milan last season.
"Cruyff was such an influence, and was fantastic for me, but now I am very proud to be facing the challenges of the Premier League". I signed for three years so normally I want to stay for three years - that means it would be going well.
'Also for the fans, we must try to be attractive.
By making young players the cornerstone of his successful Ajax team, Frank de Boer helped lay the foundations for the reawakening of one of European soccer's most storied clubs.
Speaking alongside chairman Steve Parish at a press conference, De Boer added: "The club can still grow further and further, because every year English clubs spend a lot of money, so it is possible to do something well".
De Boer will assess his back room staff over the next week before formally meeting the plays on Friday, and laying down his blueprint for the future.