The decision comes after the club concluded its internal investigations into allegations of attempted rape, assault and coercive control levelled against Greenwood in January 2022.
The 21-year-old was arrested by Greater Manchester Police (GMP) on January 30 2022 after pictures and videos detailing physical abuse against an 18-year-old lady believed to be his girlfriend were posted on social media.
The couple welcomed their first child last month.
Greenwood had been suspended from all first team activities by Manchester United since the allegations came to light.
The Crown Prosecution Service(CPS) announced in February this year that all criminal proceedings against Greenwood had been dropped.
A statement issued by United on Monday read: "Based on the evidence available to us, we have concluded that the material posted online did not provide a full picture and that Mason did not commit the offences in respect of which he was originally charged.
"That said, as Mason publicly acknowledges today, he has made mistakes which he is taking responsibility for.
"All those involved, including Mason, recognise the difficulties with him recommencing his career at Manchester United.
"It has therefore been mutually agreed that it would be most appropriate for him to do so away from Old Trafford, and we will now work with Mason to achieve that outcome."
A statement issued by Greenwood on Monday read: "I want to start by saying I understand that people will judge me because of what they have seen and heard on social media, and I know people will think the worst.
"I was brought up to know that violence or abuse in any relationship is wrong, I did not do the things I was accused of, and in February I was cleared of all charges. However, I fully accept I made mistakes in my relationship, and I take my share of responsibility for the situations which led to the social media post.
"Today's decision has been part of a collaborative process between Manchester United, my family and me.
"The best decision for us all, is for me to continue my football career away from Old Trafford, where my presence will not be a distraction for the club."
Greenwood came through the Manchester United academy and made 129 first team appearances, scoring 35 goals.
He has one cap for the England national team.