Chelsea have strengthened their defensive options by completing the signing of Antonio Rüdiger on a five-year contract from Roma, with the Germany defender joining the Premier League champions for an initial £29m.

The fee for the 24-year-old could rise as high as £34m with add-ons for a player who has won 17 caps for Germany and made four appearances in their triumphant Confederations Cup campaign in Russia, including starting in the final against Chile, which they won 1-0.

Rüdiger moves to England after two years at the Serie A club, whom he initially joined on a season-long loan from Stuttgart, and will help fill the void left by John Terry’s departure for Aston Villa under freedom of contract. Chelsea also sold Nathan Aké to Bournemouth for £20m.

“It’s a great feeling because not every player has the opportunity to join a huge club like this,” Rüdiger said. “I am looking forward to meeting up with my new team-mates and I’m very proud to officially become a Chelsea player.”

The Chelsea manager, Antonio Conte, had made clear the need to reinforce the team’s back-line in readiness for their return to the Champions League, and had initially hoped the club would succeed in luring either Virgil van Dijk or Leonardo Bonucci to Stamford Bridge.

Yet the valuations placed on those players by Southampton and Juventus respectively had prompted Chelsea to consider other options with Rüdiger, for all that he cost Roma an initial £3.5m plus a further £7.9m when making his move permanent last summer, a more attractive option.

“We are pleased to be able to bring in a player of proven quality who adds to our defensive options,” the Chelsea technical director, Michael Emenalo, said. “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.”

Rüdiger, who was the subject of racial abuse by Lazio fans at the Rome derby in March, has most often been used at centre-half, but could operate at right-back if required. The 6ft 3in defender would appear to be competing most obviously with César Azpilicueta as the right-sided of Chelsea’s three centre-halves in Conte’s favoured system, though the Italian is hoping to have at least two senior players competing for each place in his starting lineup.

Terry, who has signed an initial one-year deal at Villa Park, was only a bit-part player last season and could yet be followed by Kurt Zouma in departing the club, despite the 22-year-old French defender apparently being resistant to a loan move. Chelsea have also welcomed the talented young defender, Andreas Christensen, back from a two-year loan spell at Borussia Mönchengladbach to bolster their options.

Conte has been frustrated this summer at the club’s apparent toils in the transfer market, with Willy Caballero, who moved on a free transfer from Manchester City, and the teenager Ethan Ampadu, from Exeter City, Chelsea’s only arrivals prior to Rüdiger. Meanwhile, a deal has been agreed in principle for the Monaco midfielder, Tiemoué Bakayoko, for around £40m and negotiations continue with Juventus over their left wing-back, Alex Sandro, who would cost a club record £61m.

Chelsea had hoped to eclipse any club record again by re-signing the striker Romelu Lukaku from Everton before the player opted to join Manchester United. Conte had targeted Lukaku as his first-choice replacement for the outgoing Diego Costa and while his exasperation was initially made clear to the Chelsea hierarchy, who failed to complete a deal for the Belgian, his ire is now increasingly directed at the player and his agent, Mino Raiola.

The champions must now decide whether to reignite their long-standing interest in Real Madrid’s Álvaro Morata – who had previously been targeted by United – or bid for the Torino forward, Andrea Belotti, whose buy-out clause is set at £87m. There is interest, too, in Arsenal’s Alexis Sánchez though the hierarchy at the Emirates stadium would be reluctant to lose the Chilean to rivals from across the capital.