The 23-year-old Spanish goalkeeper put pen to paper on a seven-year contract with the west London club last week after the Blues agreed to sell Thibaut Courtois to Real Madrid.
The goalkeeper signed for the west London side from Athletic Bilbao and he will now be hoping to swiftly adapt to the rigours of English football.
And the shot-stopper has admitted that he is relishing the chance to prove himself at Stamford Bridge as he gets used to his new life in London.
Speaking in an interview with Chelsea FC’s website, he said: “I’m incredibly happy to be here, this is a great challenge for me and it means a lot in my career and personal life.
“It’s a great step forward in my career, and very brave of the club to take me in. In terms of the price, it’s something I don’t think about. I just want to be myself, the same as I’ve always been, and try to give my best for the club.
“I came back from my holiday on 23 July and a few days into my training I knew about Chelsea’s interest in me.
“There had been prior offers but Athletic are a club that doesn’t usually take an interest in these transfers. I’ve been aware of the interest Chelsea had for a few weeks now.”
Chelsea FC will be looking to challenge for the Premier League title this season after they finished in a disappointing fifth place last term.
The Blues have since brought in new boss Maurizio Sarri to replace Antonio Conte after they chose to sack the Italian manager last month.
Chelsea FC will have to settle for Europa League football this season after they ended up fifth and missed out on a spot in the Champions League for this term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news