The Germany defender completed his move to the Blues from Roma over the weekend.
Chelsea’s new signing Antonio Rudiger will not be with the Premier League champions as they begin their pre-season on Monday when all eyes will be on Diego Costa.
Germany international defender Rudiger signed a five-year deal with the Blues on Sunday, leaving Roma for a fee of £29million that could rise to £33.3m.
Rudiger is set for some additional time off as a result of Germany’s recent Confederations Cup final win but the majority of Antonio Conte’s squad are due to return to pre-season training.
Striker Costa, who was reportedly told he was surplus to requirements by the manager in a text message sent last month, is due to report back to their Cobham base despite uncertainty about his future.
The Spain international has been linked with a return to Atletico Madrid, although their current transfer ban means they cannot officially register anyone to play until January.
With Chelsea set to miss out to Manchester United for Romelu Lukaku, despite them being the favourites to re-sign their former player, Conte may have to find a way to reintegrate Costa into his squad as without him it leaves only Michy Batshuayi as a senior striker.
In Rudiger, though, Conte has his first major signing of the summer.
“It’s a great feeling because not every player has the opportunity to join a huge club like this,” the defender told chelseafc.com. “I am looking forward to meeting up with my new team-mates and I’m very proud to officially become a Chelsea player.”
Chelsea’s only other signing so far this summer is Manchester City’s out-of-contract goalkeeper Willy Caballero.
“We are pleased to be able to bring in a player of proven quality who adds to our defensive options,” said technical director Michael Emenalo.
“Antonio is still young but is experienced at club and international level and possesses all the requisite attributes to thrive in the Premier League.
“We have been aware of him for some time and we are confident he will fit in well with the squad.”