Rudiger has spent the last two seasons in Serie A, arriving at Roma on loan from VfB Stuttgart in 2015 before making a permanent switch at the end of the campaign.
"It's a great feeling because not every player has the opportunity to join a huge club like this," Rudiger, who will wear the number two shirt, said in a statement.
"I am looking forward to meeting up with my new team mates and I'm very proud to officially become a Chelsea player."
The 24-year-old Germany international has won 17 caps since his debut in 2014.
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Manager Antonio Conte is looking to strengthen the Chelsea side that lifted the league title in his first campaign at Stamford Bridge.
Rudiger is the London club's second signing of the transfer window after goalkeeper Willy Caballero joined as a free agent from Manchester City.
Chelsea will kick-off their 2017-18 league campaign at home against Burnley on Aug.12.
(Reporting by Hardik Vyas in Bengaluru)
