The 24-year-old has signed a five-year contract and will wear the No.2 shirt.
The defender said: ‘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.’
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.’
A tough tackler, Rudiger is quick on his feet and a commanding presence in the air. Having spent most of his career playing in central defence, he is equally comfortable at full-back.
Born in Berlin, Rudiger spent time in the youth set-up at Borussia Dortmund before moving to Stuttgart.
He made his Stuttgart debut in a 2012 game against Borussia Monchengladbach at the age of 18, and firmly established himself as a first-team regular during the 2013/14 campaign.
In 2015 he moved to Roma, initially on loan, and after a successful maiden season in Serie A the deal was made permanent.
Rudiger arrives at Stamford Bridge having acquired European experience in both the Champions League and Europa League.
He featured frequently for Germany at youth level and made his debut for the senior side in a friendly against Poland in May 2014.
Having been called up to the reigning world champions’ Euro 2016 squad, Rudiger subsequently missed the tournament through injury but he was a key performer in Germany’s recent Confederations Cup victory in Russia. He was part of the defence which kept a clean sheet in the 1-0 win over Chile in last Sunday’s final.
We look forward to him joining up with his new team-mates ahead of the 2017/18 campaign.