The 26-year-old left boyhood club Atletico Madrid on deadline day to complete a season-long loan move to Stamford Bridge.
Speaking to the club's website, Saul said: "I am so happy to be here. It was a great opportunity for myself and for my career. I had to take the chance to be here at Chelsea so I'm very happy and very excited.
"I'm really looking forward to training and, most importantly, to start working with my coach."
"The last day of the transfer window was crazy but in the end I could come here, as we all were hoping, so I have to seize this chance.
"Since I was a child, I always had two goals - to make history at Atletico Madrid and to play in the Premier League, not only because of the league itself but also for its culture and the language."
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