The La Liga champions announced yesterday that they have agreed a deal with the Blues for the sale of Luis.
The 28-year-old, who spent four years at the Vicente Calderon, has admitted that it was a tough decision to make, but insists that he needed a change.
"I can say that it has been the most difficult decision I've ever made in my life," Luis told reporters.
"When the first offer from Chelsea came, the first thing I did was talk to [Jose Luis] Caminero and the club and explain my reasons.
"The truth is that as a child I always dreamed of playing in the Premier League, and decided to communicate it to the club so they could see that that was my goal, a change of scenery. I think that my time here was up at this stage."
Luis was identified as a target for Chelsea following Ashley Cole's free transfer to Roma.