The 30-year-old's future had been the subject of speculation as his previous deal entered its final season.
"I am delighted to have signed a new contract," Young said.
"The spirit and motivation amongst this team is very high and we are all determined to make this a season to remember
All I have ever wanted to do is play football and to be able to continue to do that at the biggest club in the world means everything to me and my family."
Young has scored 13 goals in 115 appearances since joining United from Aston Villa in 2011, helping them lift the Premier League title in 2013
He played in a number of positions last year, deployed at wing-back when Louis van Gaal used a 3-5-2 formation, and kept his place ahead of the now departed record signing Angel di Maria once a 4-3-3 formation was adopted
Van Gaal said: "We are delighted that Ashley has signed a new contract
Ashley is a very multi-functional player
He took to the wing-back position with great confidence and flourished on the wing throughout last season
Ashley is always very professional and has a great presence in the dressing room
"
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Source: PA