The versatile Young, 33, had only a few months left on his existing deal but had stated his desire to stay at Old Trafford.
The England international joined United in 2011 from Aston Villa and has made 227 appearances for the club, scoring 17 goals and winning a clutch of trophies including the Premier League and Europa League.
He has established himself as a key member of the United squad and has made 25 appearances this season, scoring once.
Last year Young, whose contract will keep him at Old Trafford until the end of the 2019/20 season, helped England reach the semi-finals of the World Cup, and he has been capped 39 times.
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