The England international, 34, has put pen to paper on a deal until the summer with the option of a further season with Inter after the clubs agreed a 1.5 million euros (£1.3m) fee.
"Ashley Young is officially an Inter player," Inter confirmed on their official website.
"The 34-year-old English defender arrives from Manchester United and has signed a contract lasting until June 30 2020 with an option to extend for a further season."
Young becomes the third English player to join Inter following Gerry Hitchens, who moved to the Serie A giants from Aston Villa in 1961, and former United midfielder Paul Ince, who spent two seasons with the Nerazzurri after signing in 1995.
Inter signed Romelu Lukaku from United last summer, while former Old Trafford team-mate Alexis Sanchez is currently on loan there.
Stevenage-born Young, who has won 39 England caps, began his career at Watford and joined United from Aston Villa for £17million in June 2011.
He made 261 appearances for the Red Devils, scoring 19 goals.
Young, who has been United's club captain in recent seasons, won a Premier League winner's medal in 2012-13, in Sir Alex Ferguson's final season as manager. He also picked up winner's medals in the FA Cup, League Cup and Europa League.
He tweeted on Friday night: "Very excited to join Inter and begin this new challenge. Can't wait to get started."
Inter added: "As a keen campaigner against racism, Young has led from the front for Manchester United - recently wearing the captain's armband for the past three seasons.
"However, he's now ready for a new adventure and on behalf of the entire Nerazzurri family, we'd like to wish our new signing all the very best."
United said in a statement: "Everyone at the club would like to thank Ashley for his many seasons of service and to wish him well for the future."
Follow Sporting Life on social media - find us on Facebook here or tweet @SportingLifeFC
Related football links
