The former England worldwide, who joined Manchester United back in 2011, only registered 18 appearances in all competitions with The Red Devils this term. While the former played as a striker from 1961 to 1963 and scored 20 goals in 43 matches, Ince played between 1995 and 1997 and made 73 appearances.
"Ashley Young is officially an Inter player", the club said in a statement.
Inter have handed Young, 34, a contract until the end of the season, though the deal includes an option for it to be extended by a further year.
Young, who in recent years has predominantly played at left-back but can also play on the wing, joins former United teammates Romelu Lukaku and Alexis Sanchez at the San Siro. Thank you for your support during the highs and the lows. Inter now lie second in Serie A - two points behind champions Juventus.
"To be truthful, I believe it was once for Ashley, he's 35 in the summertime and if he will get a two-year contract someplace I believe it's as much as him to take that", Solskjaer mentioned.
"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". At the Old Trafford, he has won one Premier League (2012/13, Sir Alex's last league title), one FA Cup, one League Cup, three Community Shields and one Europa League.
"We will give him the absolute amount of time to find out", said Solskjaer. "We got a transfer fee for someone who's been so loyal to the club".
Maguire will wear the armband for the first time as United's permanent skipper against champions-elect Liverpool on Sunday.