The club said: "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."
But the Countdown presenter said whilst the decision by United was “right”, the statement made about Greenwood’s departure was “horrendous”.
The Jewish TV star also said the club's chief executive officer Richard Arnold should consider his position over the case.
She said on Twitter: “Right decision, horrendous statement.
Mason Greenwood was a forward at Manchester United (Photo: Getty)
“The only people in a position to ever assert guilt or innocence re domestic abuse allegations are trained, qualified, experienced experts.
“This goes far beyond the scope of what Manchester United were tasked with."
Speaking on The News Agents podcast, she was asked if Arnold should consider his position.
The TV presenter, who shares daughters Maven and Noah with former Strictly Come Dancing professional Pasha Kovalev, replied: "Yes I do. I say this with such a heavy heart.
"As a fan I grew up - these players are heroes for little kids, they're your heroes.
"I did Manchester United as my subject on Mastermind, I've been lucky enough for work to go to the club to do charity events, to meet the players, to meet the manager, to go to the director's box for matches, it's like my ultimate dream and I would love more than anything else in the world to give that to my daughters, but I can't not speak out.
"What I risk as a fan, or as someone who gets all these privileges, compared to what a domestic abuse victim survivor risks by coming forward even though she or he might not be believed, it is nothing.
"But I just don't agree with what's happened at all."
Manchester United's chief executive officer Richard Arnold (Photo: Getty)
Riley previously said she would not be able to continue supporting Manchester United if Greenwood remained there and has now branded the handling of the situation as a "disgrace".
It was reported last week that chief executive Richard Arnold told the club's executive leadership in early August that United were planning to bring Greenwood back.
That story and further information led increased pressure on the club, with Arnold publishing a public letter to supporters upon the conclusion of their in-house investigation.
After the charges were dropped, Manchester United conducted its own investigation, saying the club had "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", but added that the player had publicly acknowledged "he has made mistakes which he is taking responsibility for".
Riley went on to say the club had "greenlighted" social media abuse of the alleged victim.
She said: "I think it's been absolutely mismanaged. I've been a Man Utd supporter since before I was born.
“My dad's been going since 1960s, I had my babies' Man Utd stuff ready when they were in the womb and I've never been more ashamed of the club. It's a disgrace.
"They had another opportunity to make it right, and they have just greenlighted the abuse that's been going on on social media, to claim innocence, to turn the alleged abuser into the alleged victim, which is classic DARVO (Deny, Attack, and Reverse Victim and Offender) techniques and I'm so disappointed."
