The 21-year-old forward faced allegations of attempted rape, controlling and coercive behaviour and assault. All three charges related to the same woman.
The Crown Prosecution Service (CPS) said it had a “duty to stop the case” following the “withdrawal of key witnesses and new material that came to light.”
Those developments meant there was “no longer a realistic prospect of conviction,” it added.
“In these circumstances, we are under a duty to stop the case. We have explained our decision to all parties.”
The investigation began just over a year ago, in January 2022. A trial date had been set for November 27 this year.
In a short statement released on his behalf, Greenwood said, “I am relieved that this matter is now over and I would like to thank my family, loved ones and friends for their support.
“There will be no further comment at this time.”
A Manchester United statement read, “Manchester United notes the decision of the Crown Prosecution Service that all charges against Mason Greenwood have been dropped.
“The club will now conduct its own process before determining next steps. We will not make any further comment until that process is complete.”
Sky Sports News understands Greenwood will not be returning to training or playing while the process takes place.
Greater Manchester Police (GMP) said the decision to drop the charges had “not been taken lightly.”
Chief Superintendent Michaela Kerr, GMP’s head of public protection, said it was “only fair” that the force publicised the latest development given the “significant media coverage of this case.”
She added, “The investigation team has remained in regular contact with the legal team, providing any updates of note, and so understand the rationale for the discontinuation of proceedings at this stage, and that this decision has not been taken lightly.
“Despite the media and public’s interest in this case, we have decided not to comment on it in any further detail.”
Ms Kerr did however appeal to people who felt they were, or might have been, a victim, reiterating GMP’s “commitment to investigating allegations of violence against women and girls.”
She continued, “An ever increasing number of officers are receiving specialist training and the force is more consistently utilising tools, available via the criminal justice system, to keep people safe and care for victims.”
“If you feel you are or might be a victim, please don’t let this case put you off asking for help.”
United announced on January 30 last year he would not return to training or play any matches “until further notice”.
Nike also suspended and later terminated its sponsorship deal with Greenwood, while Electronic Arts confirmed he had been removed from active squads on its FIFA 22 game.
The Bradford-born player came through the United academy and made his senior debut in a Champions League victory away to Paris Saint-Germain in March 2019.
He has one senior cap for England, playing in the Nations League match against Iceland in September 2020.