The deal, which is worth £43.7m plus potentially another £3.4m in add-ons, was confirmed on Thursday night according to MailOnline.
Onana flew to the US on Thursday to join up with his new teammates on tour after passing a medical at Carrington.
Onana said goodbye to Inter fans after one year at the San Siro in which he helped the club reach the Champions League final as well as winning the Italian Cup and Super Cup.
Posting a video montage of himself in action for Inter, Onana wrote: ‘I never imagined that a farewell would be so hard.Onana flew to the US on Thursday to join up with his new teammates on tour after passing a medical at Carrington.’A year ago I became a Nerazzurro, many people told me that this club and this city had something special. Now I can confirm it. In my first days as a Nerazzurro I realised that this is a family, that being Interisti is a way of understanding life.
‘I fell in love with San Siro, La Curva and the city. Now the circumstances are right for me to start a new journey in Manchester. I do it with great enthusiasm, but knowing that I will miss you. Eternal gratitude to all the Interisti. You make this club great.
‘A year ago I became a Nerazzurro, many people told me that this club and this city had something special. Now I can confirm it. In my first days as a Nerazzurro I realised that this is a family, that being Interisti is a way of understanding life.
‘I fell in love with San Siro, La Curva and the city. Now the circumstances are right for me to start a new journey in Manchester. I do it with great enthusiasm, but knowing that I will miss you. Eternal gratitude to all the Interisti. You make this club great.