The transfer is reported to involve an upfront £25m payment, with an additional sell-on clause included.
Chelsea’s co-sporting directors Paul Winstanley and Laurence Stewart told the club website: “We’re very pleased to welcome Robert to Chelsea and he adds further quality to our goalkeeping unit.
“Robert has repeatedly proved himself in the Premier League and been capped by his country. We are excited to watch him work with (head coach) Mauricio (Pochettino) and his coaching team during the season ahead.”