The move had been expected after Albany County prosecutors said they could not prove the case and intended to drop it.
Cuomo, who denied the allegation he groped an aide in the executive mansion in 2020, did not speak during Friday's short hearing, held with the judge sitting in an Albany courtroom and the lawyers and defendant appearing via videoconference.
"As the governor has said, this simply did not happen," his lawyer Rita Glavin said in a video statement after the hearing.
"Today, reason and the rule of law prevailed. Not politics, rhetoric or mob mentality."
During the hearing Assistant District Attorney Jennifer McCanney told the judge prosecutors had reviewed the evidence "and concluded we cannot successfully secure a conviction in this case".
Cuomo could still face lawsuits if his accusers choose to take him to court. Some have indicated they plan to do so.
Cuomo's spokesman Rich Azzopardi said on Friday the former governor "will not pay one penny in attempts at civil extortion".
Albany County District Attorney David Soares said this week that although the aide was credible, and some evidence supported her account, he believed he could not win a conviction.
The aide, Brittany Commisso, said Cuomo slid his hand up her blouse and grabbed her breast when they were alone in an office at the mansion.
Her testimony was among the most damning in a report released in August by Democratic state Attorney General Letitia James that concluded Cuomo sexually harassed 11 women.
Cuomo resigned that month but insists he never touched anyone inappropriately.
In a letter to the judge on Tuesday, Soares said "statutory elements of New York law make this case impossible to prove".
He added government inquiries into Cuomo's conduct had created "technical and procedural hurdles" regarding prosecutors' obligations to disclose evidence to the defence.
Cuomo's lawyer Glavin on Friday called the complaint "a blatant political act" and assailed Commisso, saying no jury would have found her credible.
Commisso did not respond to a request for comment, made through her lawyer on Friday, but earlier this week she blasted Soares for giving up on the case.
"My disappointing experience of re-victimisation with the failure to prosecute a serial sexual abuser, no matter what degree the crime committed, yet again sadly highlights the reason victims are afraid to come forward, especially against people in power," Commisso said in a statement on Tuesday to the Times Union of Albany.
Two prosecutors in the New York City suburbs separately announced last month Cuomo would not face charges for allegations involving other women who said they had been subjected to unwanted kisses or touches.
