The Atletico Madrid midfielder is on loan at the Stamford Bridge club for the season.
There is an option in the deal for Chelsea to make the move permanent.
Saul secured his switch during the last minutes of the transfer window on Tuesday night.
He told the club's website after signing: "The language is a big challenge for me and I want to learn it as soon as possible in order to be able to communicate with my team-mates simply and comfortably.
"At Atletico I used to speak with [Kieran] Trippier but my English isn't good enough.
"I don't even dare to do interviews in English!"
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