The 22-year-old joins the Eagles following a prolific spell at Midtjylland, where he has scored 15 goals and created nine more in 26 appearances this season.
"[Palace is] a big club with ambition, a good club who takes good care of its players," Sorloth told the Palace website. "It feels amazing, it's a dream come true to play in the Premier League. I've dreamt about this since I was six years old.
"My short term aim is to try get my debut as quickly as possible, show my skills on the training ground - and hopefully the manager likes what he sees."
Sorloth, who will wear the number nine shirt, joins a Palace side that are 13th in the Premier League table and three points above the dropzone.