On Sunday morning, it was revealed that the 24-year-old, who helped Germany win this summer's Confederations Cup, had travelled to London to complete a medical ahead of a £33m move to Stamford Bridge.
The transfer has now been completed, with Rudiger signing a five-year contract with the Premier League champions.
"It's a great feeling because not every player has the opportunity to join a huge club like this," Rudiger told the club's official website. "I am looking forward to meeting up with my new teammates and I'm very proud to officially become a Chelsea player."
Meanwhile, Chelsea's technical director Michael Emenalo added: "We are pleased to be able to bring in a player of proven quality who adds to our defensive options.
"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."
The centre-back will wear the number two shirt for Chelsea during the 2017-18 campaign.