The announcement comes just one day after Erik ten Hag was let go by the team, as Manchester United currently sits in 14th place in the Premier League standings. The new Portuguese coach is expected to make his debut during Sunday's league match against Leicester City at Old Trafford.
"Manchester United FC expressed interest in hiring coach Ruben Amorim, with Sporting's board of directors referring to the terms and conditions set out in the employment contract in force between the company and the coach, specifically the respective termination clause and for the amount of Euro 10,000,000," a statement from the Lisbon-based club said.
The 39-year-old Amorim, who emerged as a front-runner soon after Ten Hag's sacking, led Sporting to the Primeira Liga title in 2021, ending a 19-year league title drought, before winning a second last season.
Portuguese media reported his final game with Sporting would be on Oct 29 evening against Nacional.
Amorim had been heavily linked with replacing Juergen Klopp at Liverpool last season with the club choosing to hire Arne Slot instead. He also held talks with West Ham United to replace David Moyes before opting to remain in Lisbon.
His appearance in London for talks with West Ham, just ahead of Sporting's clash with rivals Porto, did not go down well with Sporting fans. He subsequently apologised for his actions.