The 25-year-old uncapped Spaniard moves to the Premier League for the third time in his career.
"It's a step up in my career and I think this is the perfect place for me to continue developing. It's time for me to win some titles.
'It was an easy decision for me to make when I heard the club were interested in signing me.
"My family and close friends know Chelsea is the club I have dreamed about playing for so I'm really excited about the challenge and I'm looking forward to working with my new team-mates."