The 22-year-old German, born to a German father and mother from Sierra Leone, is considered one of the most promising talents in the Bundesliga and has already made six appearances for the German national side.
"I'm absolutely delighted to be able to wear the Roma jersey," Rudiger told Roma TV.
"I've come here to win titles, to win the scudetto. I would like to thank all the Roma fans and promise them that I will give everything for this club."
Roma coach Rudi Garcia admitted earlier this week he had concerns over his defence and Ruediger's arrival should calm concerns following French defender Mapou Yanga-Mbiwa's recent departure for French side Lyon.
Ruediger represented the German national team at various levels before making his senior international debut for Joachim Loew's side on May 13, 2014, when he was just 21 years old.
Roma, distant runners-up to champions Juventus last season, open this season's Serie A campaign away to Verona in Saturday's early game.