Chelsea have taken their weekly spend to almost £74m, and eased Antonio Conte’s transfer frustrations in the process, by completing the signing of Tiemoué Bakayoko from Monaco in a deal worth up to €45m (£39.7m).

The France international signed a five-year contract with the Premier League champions on Saturday having undergone a medical 24 hours earlier.

The midfielder is Chelsea’s second expensive recruit in the past week after the defender Antonio Rüdiger’s arrival from Roma for £34m, the Stamford Bridge club moving on swiftly from the disappointment of being beaten to Romelu Lukaku’s signature by Manchester United.

While the pursuit of a new striker to replace Diego Costa continues, there will be relief at Chelsea having secured two key targets for Conte in quick succession. Bakayoko claimed to have fulfilled a childhood ambition by joining the champions, but is believed to be six weeks away from first-team contention having had keyhole surgery for a minor knee problem at the end of last season.

“Tiemoué was outstanding as Monaco emerged as one of Europe’s best sides last season and we are delighted to welcome him to Chelsea,” said Michael Emenalo, the champions’ technical director. “Despite his young age he already has plenty of experience as a French title winner and having competed in the latter stages of the Champions League, we believe he will add considerable quality to our squad.”

Antonio Conte pictured speaking to his new signing at Chelsea’s Cobham training base on Friday. Photograph: Darren Walsh/Chelsea FC via Getty Images

The 22-year-old, who will wear the No14 shirt for Chelsea, said: “I am very happy to be here and to join this great team. I have grown up watching Chelsea. Signing was the natural thing for me because it is a club I loved very much in my childhood. I am now looking forward to evolving under this fantastic coach and alongside so many great team-mates.”

Bakayoko was a key figure for Monaco as they won the French title and reached the Champions League semi-finals last season, scoring the goal that eliminated Manchester City in the last 16 of the competition. His form earned him a first call-up to the France squad in March when he partnered new Chelsea team-mate N’Golo Kanté in midfield in a friendly defeat by Spain. His arrival will prompt the departure of Nemanja Matic from Stamford Bridge, with the Serbia midfielder having been given permission to miss the club’s pre-season tour of China and Singapore amid interest from Juventus, Inter and Manchester United.