The 21-year-old was arrested in January 2022 amid allegations surrounding images and videos.
He was later charged with attempted rape, controlling and coercive behaviour and assault occasioning actual bodily harm.
The Crown Prosecution Service said the charges were discontinued after key witnesses withdrew their involvement.
A spokesman said: "We have a duty to keep cases under continuous review.
"In this case a combination of the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction. In these circumstances, we are under a duty to stop the case.
"We have explained our decision to all parties.
"We would always encourage any potential victims to come forward and report to police and we will prosecute wherever our legal test is met."
Within hours of the allegations surfacing at the beginning of 2022, the forward, who has made one appearance for England, was suspended from playing or training with the Old Trafford club.
The club has been asked by the BBC to comment.
Greater Manchester Police said it was "only fair" to announce Greenwood would no longer face criminal proceedings.
Greenwood came through United's youth academy and made his full debut in 2019 aged 17. He was a key member of the first team last season, making 18 Premier League appearances, the last of which was on Jan. 22 against West Ham United, before being suspended.
He made one appearance for England in September 2020.
In February 2022 Nike ended its sponsorship with Greenwood following the accusations, while he was also removed from some versions of the FIFA 22 video game.
Mason Greenwood Photo: PHOTOSPORT