Palace boss Roy Hodgson had previously registered his interest in Tosun.
"We're delighted to have secured Cenk's services," Palace chairman Steve Parish said.
"We've enjoyed a great first half of the campaign and Cenk's arrival will bolster our squad as we push for a top-half Premier League finish. Cenk has a proven record as a goalscorer and we've admired him for some time."
Tosun has scored once in eight appearances in all competitions for Everton this season, taking his tally to 10 in 51 games.
He is available to play for Palace as they host tenth-placed Arsenal - the team directly below them - in the Premier League on Saturday.