Kepa was officially unveiled at the club this afternoon, and he has already set his sights on helping the Blues to silverware under new boss Maurizio Sarri.
"I am incredibly happy to be here. It's a great challenge to me and means a lot. It's a great step forward in my career," he told reporters at a press conference.
"Some players take more time to adapt, some less. I hope I will be able to adjust and adapt as soon as possible. I realise the game in England is different, but I have been given fantastic references by other Spanish players in this league. I am a player who demands a lot from myself.
"Over the next seven years, I expect to achieve a great growth, personally and collectively, and I hope we will win many, many titles. A new stage is starting for me, and I am really happy to start this new stage in my career and my life."
Kepa, who replaces Thibaut Courtois in the Chelsea goal, could make his debut for the club away to Huddersfield Town on Saturday.