Campana has been with Sevilla since the age of seven, progressing to their senior side in 2011.
He played only five times in La Liga last season, ending the season on the injured list after suffering a fracture in his foot.
But Campana was fit in time to play for Spain's U20 side at the World Cup in Turkey, where his performances were enough to make him a coveted player for a number of clubs across Europe.
Campana told Palace's official website: "I'm delighted to become a Crystal Palace player. Over the last two years, I've had some problems with my hometown club, but I'm really excited to play in the Premier League.
"I think it's a good step for me and I'm really excited and looking forward to meet all the boys and start as quickly as possible.
"I got the first interest through my agent, who said that Crystal Palace were interested and straight away I said 'yes' because for me it was a dream to play in England, especially in the Premier League. I hope to help the team stay in the league and then move forward.
"What I like to think are my best qualities are to keep the ball and to have good distribution. I have always been a typical Spanish midfielder and I like to move forward and score goals.
"I scored a lot of goals when I was in the academy at Sevilla. That's what I want, but especially to keep the ball and to organise the team."