He admitted exchanging online messages with the girl beginning in January 2015 and "sharing explicit images and encouraging her to engage in sexually explicit conduct".
The Times, quoting two people close to the situation, reported that Weiner will plead guilty to a single charge of transferring obscene material to a minor.
In a written plea agreement, prosecutors said aggravating factors such as the age of the victim would have called for a prison sentence of up to 14 years under sentencing guidelines were it not for the plea bargain and a 10-year maximum penalty on the charge.
Weiner was already in federal custody ahead of the court hearing, which was scheduled for at 11 a.m.
The investigation into Weiner came to light after the Daily Mail, a British newspaper, published an interview with the North Carolina teen previous year.
Weiner (52) entered his plea before USA district judge Loretta Preska shortly after 11am (4pm Irish time).
Weiner, a Democrat who represented a New York City congressional district, resigned from his House seat in 2011 after he accidentally tweeted an explicit photo of himself that he had meant to send to a supporter.
A spokesman for the law firm representing Weiner, Covington & Burling, said he would plead guilty before U.S. District Judge Loretta Preska on Friday morning but offered no further details.More news: GOP lawmaker says Trump allegations, if true, are grounds for impeachment
In court, the 52-year-old former Democratic congressman paused repeatedly as he fought back tears and tried to compose himself. The two married in 2010, and in June 2011 Weiner resigned from Congress, a month after the release of an explicit photo of him that he inadvertently posted on his Twitter account.
As part of his plea, Weiner agreed to forfeit his iPhone.
He surrendered to police this morning and appeared in court at 11am local time (4pm GMT), according to the Federal Bureau of Investigation.
It is alleged that Weiner shared "rape fantasies" with the girl, and asked her to dress up in school uniform during their Skype conversations, which went on for several months.
"I have a sickness, but I do not have an excuse", Weiner said, apologizing to the 15-year-old girl to whom he sent sexually explicit images and messages last year.
Many Democrats, including Clinton, have said the timing of the announcement that the investigation had been renewed contributed to her November loss. Trump and other Republicans accused Clinton of endangering national security by exposing classified information to potential hacking.
In September, Weiner suggested he had "likely been the subject of a hoax" after the accusations of sexting with the teen first surfaced. Weiner's online behavior first cost him his career in Congress, but he was on the verge of a comeback win in the Democratic primary for NYC mayor when his continued sexting was revealed despite earlier pledges he had overcome the compulsion.