Milan, who are Chelsea’s next American pre-season tour opponents in Boston on Sunday, have signed Italian pair Christian Vieri and Alberto Gilardino rather than meet Chelsea’s demands for extending Crespo’s deal.

But that adds up to good news for Chelsea, according to Mourinho.

“Now he wants to prove himself in the Premiership. I’m so happy because we could not have got a better player than him,” said the manager.

Crespo seemed initially reluctant to rejoin Chelsea, having found it difficult to adapt to English football during the 2003/04 season, when Claudio Ranieri brought him to the club from Inter Milan.

With Milan he was part of a team who finished runners-up in both the Champions League and Serie A, and his family were settled in the city, making it a wrench to return to Stamford Bridge.

But Crespo’s focus has returned after a week and a half in the company of his team-mates, and Mourinho expects the 30-year-old’s return to be a success.

“I understood his desire to stay in Italy because it was not for sporting reasons,” said the former Porto boss.

“I spoke to him on his holidays for a few days in Sardinia. He’s happy with his work and he’s happy at Chelsea, which has changed a lot.”