The 22-year-old has signed a seven-year contract with the Blues. He arrives for a fee of £20m.
"I am very happy with how the last 12 months have panned out," he told chelseafc.com. "I am very confident in myself and I know what qualities I have.
"Luckily I had the chance to show myself on the biggest stage in Spain and now I am very happy to have the chance to do that at one of the biggest clubs in the world.
"I always liked watching Chelsea because I watched a lot of Petr Cech growing up, so Chelsea were one of my favourite teams to follow."
On the competition he faces, Jorgensen added: "Robert Sanchez has been with the national team of Spain, where I live, and I followed him a bit when he was at Brighton and now Chelsea.
"I know he is a very good goalkeeper and I hope we can learn from each other and produce the best versions of ourselves together."