Antonio Conte is convinced he can restore Chelsea to the Champions League at the first time of asking but already faces an uphill task to persuade Diego Costa to remain at Stamford Bridge next season with the Spain international intent on returning to La Liga.

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The manager of Italy has signed a three-year contract worth £5m a season, with a £5m bonus should he steer Chelsea to their second European Cup. He will take up the reins once Italy’s participation at Euro 2016 has concluded and will inherit a team who have had a traumatic season and are set to miss out on European competition of any kind for the first time in Roman Abramovich’s 13-year ownership.

Conte has already made clear to the Chelsea hierarchy his belief he can return the team – 25 points off the Premier League leaders, Leicester City, despite enjoying a 14-match unbeaten run since José Mourinho’s sacking in December – to the Champions League, though his hopes of convincing Costa to remain appear slim. The striker, who is serving his second three-game suspension of the campaign, has grown weary at the regular scrutiny of his on-field discipline in English football and has been encouraged by news that Atlético Madrid are keen to bring him back to the Vicente Calderón Stadium this summer.

The striker’s agent, Jorge Mendes, is also understood to have sounded out Paris Saint-Germain over a move for his client, who has three years to run on his contract, and there has been talk of interest from clubs in the Chinese Super League. Yet a return to Spain remains Costa’s priority and it will be an early test of Conte’s powers of persuasion as to whether the forward stays.

Conte does not intend to speak publicly again about the Chelsea job until after the European Championship but the 46-year-old is expected to visit Cobham before the end of the season to meet the squad. He has already supplied his new employers with a list of summer transfer targets and spoke at length with the hierarchy about recruitment in a meeting at a central London hotel on Monday afternoon, having formally signed a deal through to 2019.

He said: “I am very excited about the prospect of working at Chelsea. I am proud to be the coach of the national team of my country and only a role as attractive as manager of Chelsea could follow that. I am looking forward to meeting everyone at the club and the day-to-day challenge of competing in the Premier League.

“Chelsea and English football are watched wherever you go, the fans are passionate and my ambition is to have more success to follow the victories I enjoyed in Italy. I am happy we have made the announcement now so everything is clear and we can end the speculation. I will continue to focus on my job with the Italian national team and will reserve speaking about Chelsea again until after the Euros.”

Costa’s departure would leave Chelsea pursuing striker reinforcements as a priority, with Conte having already asked the club to monitor Edinson Cavani’s situation at PSG. The Uruguayan may seek to leave if Zlatan Ibrahimovic is offered new terms and remains at the French club, though Cavani will be pursued by suitors who can offer Champions League football. Gonzalo Higuaín at Napoli has also been tracked while Chelsea’s technical director, Michael Emenalo, is understood to be intent on exploring the chances of re-signing Romelu Lukaku from Everton. The Belgian’s agent, Mino Raiola, has indicated he will seek a move this summer though Everton will resist his sale.

While Conte is also pushing for the addition of Roma’s Belgian midfielder Radja Nainggolan, who is available for €35m, and further experienced defensive cover such as Leonardo Bonucci, Kostas Manolas, Kalidou Koulibaly and Antonio Rüdiger have been scouted at Juventus, Napoli and Roma respectively, where the latter is on loan from Stuttgart, it is perhaps telling he is to adopt the title head coach rather than manager. That would appear to reinforce Emenalo’s position at the club despite Chelsea’s patchy recent record on recruitment.

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Juan Cuadrado is expected to return from a year-long loan at Juventus, with whom Conte won three Serie A titles up to 2014, and the Colombian may have a key role to play in Conte’s preferred 3-4-3 formation. Chelsea could also make another attempt to sign France midfielder Paul Pogba, having had a £78m bid for him rejected last summer. There will be some departures, with neither Radamel Falcao nor Alexandre Pato likely to be offered permanent deals after loan spells and John Terry expected to end a 21-year association with the club when his contract expires in June.

Chelsea, who confirmed Conte’s appointment on the day his alleged failure to report a match-fixing scandal was heard at a court in Cremona, have given him the go-ahead to bring his long-term assistants Angelo Alessio and Massimo Carrera with him to Stamford Bridge.

Steve Holland, the assistant first-team coach, is expected to remain on the coaching staff while there will be roles for Paolo Bertelli, Mauro Sandreani and Conte’s brother, Gianluca, on the backroom team. Both the goalkeeping coach Christophe Lollichon and the fitness coach Chris Jones, will be retained.

The Chelsea chairman, Bruce Buck, hailed Conte’s “record of consistent success in his career as a manager and as a player” in a statement released on the club’s website.

“We are very pleased to have recruited one of the most highly regarded managers in world football and we are equally pleased to do so before the end of the season,” added the director, Marina Granovskaia. “This aids our future planning. I would also like to take this opportunity to thank Guus Hiddink, who has done a great job since he joined us in December.”