The Italian club reportedly agreed to pay close to £4.5m of the Chile international’s £21m annual salary, while United will pay a significant portion of his wages.
A statement on Inter’s official website read: ‘Throughout Alexis’s life, football has always represented everything, and he has always been happiest with a ball between his feet.
‘From now on he’ll have a chance to do this in Nerazzurri colours. So, on behalf of the entire Nerazzurri family, we’d like to wish him a very warm welcome and the best of luck. #WelcomeAlexis.’
Speaking on Sanchez’s football journey, Inter said: ‘Alexis had a great future ahead of him and he wanted nothing except to play football. He always said so, practically from the day he was born on 19 December 1988.
Sanchez’ move to Inter brings to an end his 18 months at United, where he scored just five goals in 45 appearances following his arrival from Arsenal.
He will now link up with former United striker Romelu Lukaku, who left the club in a £73million deal this summer.