Jorgensen, who last season became Villarreal's number one keeper, has signed a seven-year deal, Chelsea said.
The clubs did not disclose the transfer fee but British media reported the deal was worth around 20 million pounds ($25.67 million).
"This move is a dream come true," Jorgensen told the club website.
"I am very excited to have signed for Chelsea, one of the biggest clubs in the world. I can't wait to get to know everyone and to start playing with all my new teammates."
Born in Sweden to a Danish father and Swedish mother, Jorgensen represented Sweden at youth levels before making a switch to Denmark in May 2021.