The 24-year-old has agreed a five-year deal and will wear the number 2 shirt.
The defender told the club website: "It’s a great feeling because not every player has the opportunity to join a huge club like this."
"I am looking forward to meeting up with my new team-mates and I’m very proud to officially become a Chelsea player."
Meanwhile, the club's technical director Michael Emenalo said: "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."
It's official! Welcome to Chelsea, @ToniRuediger! #WelcomeRudi https://t.co/AgtH7QzFde
— Chelsea FC (@ChelseaFC) 9 de julho de 2017
'I am looking forward to meeting up with my new team-mates and I’m very proud to officially become a Chelsea player.’ #WelcomeRudi pic.twitter.com/badIXrH6NW
— Chelsea FC (@ChelseaFC) 9 de julho de 2017
Rudiger is described as a robust but athletic defender. Whilst his preferred position is centre-back, he has also shown his versatility over the years by occupying both full-back positions.
After being born in Berlin, Rudiger spent some time with Borussia Dortmund as a youngster before moving to Stuttgart, where he made his breakthrough.
He made his Stuttgart debut as an 18-year-old in 2012 and became a regular the following season.
The defender then joined Roma after a successful loan spell, however he made the decision to leave Serie A after suffering racial abuse.
Rudiger is a German international, who was part of Germany's Confederations Cup winning squad earlier this summer.
Rudiger becomes Chelsea's second senior signing of the summer after Willy Caballero. The move will come as a boost to 'Blues' boss Antonio Conte, who was said to be growing impatient with the club's inability to seal their top targets.