The La Liga champions announced earlier this week that they had agreed the sale of the 28-year-old to Stamford Bridge.
Luis told Chelsea's official website: "This move is a dream come true for me. I now have the opportunity to play for Chelsea, and also in the Premier League.
"I'm very happy and looking forward to getting started and giving my best for the team during the coming seasons."
The Blues have also added former Arsenal midfielder Cesc Fabregas to their squad from Barcelona.