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.
Sanchez who pockets an eye-watering £400,000 a week will still be United’s second-highest earner despite being on loan to Inter.
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.’
During his unveiling, the 30-year-old was seen in the Inter shirt for the first time as he posed alongside a picture of fellow Chilean Ivan Zamorano, who played for Inter between 1996 and 2001.
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.
‘His first-ever football boots were a gift from the mayor of his town, and he wore these for his first real footballing experience with Cobreloa.’
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.