Weiner's attorney, Arlo Devlin-Brown, said in a statement that the former politician "accepted full responsibility for the inappropriate, sexually explicit communications he engaged in early past year".
One of the women, Sydney Leathers, claimed Weiner sent her nude photographs and had phone sex with her. That relationship is what eventually led to the current criminal charges against him.
In a statement to CNN at the time, Weiner neither confirmed or denied sending the texts.
The plea covers conduct by Weiner from January through March of past year, the person said.
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"These destructive impulses brought great devastation to family and friends, and destroyed my life's dream of public service", Weiner said. The FBI began investigating Weiner in September after a 15-year-old North Carolina girl told a tabloid news site that she and the disgraced former politician had exchanged lewd messages for several months. "And yet I remained in denial, even as the world around me fell apart". The Daily Mail reported she said he sent her numerous photos, one of him in a pool and at least one bare-chested. "I had hit bottom".
Abedin, a top aide to Democratic presidential candidate Hillary Clinton a year ago, separated from Weiner in September after revelations he had sent more sexually charged messages online.
A message left with a representative for Abedin seeking comment Friday morning was not returned. He said the plea agreement reflected a resolution "on terms far less severe than could have been sought" because the circumstances lacked the kind of aggravating factors often present in similar cases.
The U.S. attorney's office in Manhattan said Weiner will appear in court at 11 a.m., though it would not confirm the charge or the plea. During the investigation of the illicit texts, the FBI found emails between Weiner and his estranged wife, Huma Abedin, a top aide to then-presidential candidate Hillary Clinton. The two investigations - into Weiner and into Clinton's use of a private email server - briefly collided and caused then-FBI Director James Comey to publicly reveal agents had reopened the Clinton case days before the election.
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That inquiry was brief.
Mrs Clinton partly blamed her election loss to Republican Donald Trump on Mr Comey's announcement.
In September, Weiner suggested he had "likely been the subject of a hoax" after the accusations of sexting with the teen first surfaced. His social media habits continued after leaving Congress and contributed to his poor showing with his 2013 New York City mayoral campaign, a race in which he had once been a leading contender.
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