Romelu Lukaku said Inter were the only club he "wanted" as the Belgian striker thanked Manchester United and Ole Gunnar Solskjaer in a farewell message.
Lukaku was finally granted his United exit on Thursday, joining Inter in a club-record deal reported to be €80million before the Premier League's transfer window slammed shut.
Initially linked to Antonio Conte's Inter, Serie A champions Juventus emerged as the frontrunners for Lukaku after discussing a swap deal involving Paulo Dybala, however United failed to reach an agreement with the latter.
Inter eventually negotiated a deal with United on deadline day in England and lured Lukaku to Milan on a contract until June 2024.
"Inter were the only club I wanted, because Inter is Not For Everyone. I'm here to bring the Nerazzurri back to the top," Lukaku said.
Lukaku added via Instagram: "I'm really happy to be here! Thank you for the support. Forza Inter."
The 26-year-old spent two years at Old Trafford after arriving from Premier League rivals Everton for a fee in the region of £75m in 2017, despite Conte's best efforts to bring him to Chelsea during the Italian's time in London.
Lukaku scored 12 Premier League goals in 2018-19 and 15 across all competitions as United finished sixth and lost to Barcelona in the Champions League quarter-finals last season.
Despite scoring 42 goals for United in all competitions, United were willing to part with Lukaku as manager Solskjaer preferred Marcus Rashford up front.
"To everyone involved with Manchester United - from the board to the manager and his staff, the players, and the fans. Thank you and good luck for the future @manchesterunited," Lukaku wrote on social media.
Inter – who finished fourth last season and have not won the Scudetto since 2009-10 – face Valencia in a friendly on Saturday before opening their Serie A campaign at home to Lecce on August 26.