Weiner, 52, was released on bail pending sentencing, which is scheduled for September 8, the release said.
"I accept full responsibility for my conduct".
"I have a sickness, but I do not have an excuse", Weiner said in court. He said he knew his conduct was "as morally wrong as it was unlawful". Weiner agreed to surrender his iPhone as part of the plea agreement.
Anthony Weiner, the former Democratic congressman whose "sexting" scandals ended his political career and embroiled him in a tumultuous FBI investigation of Hillary Clinton before the election, is to appear in a federal courtroom in New York City on Friday to enter a guilty plea.
During that federal investigation, at least one device used by Weiner and Abedin was discovered. But Weiner is likely to serve much less time if he is sentenced to prison.
Although the sexting went on for months, Weiner faces only a single charge, with a maximum penalty of 10 years in prison.
In court, Weiner cried as he apologized to the teenager with whom he exchanged sexually explicit texts. It was an emotional and halting allocution, and Weiner took frequent pauses for water.
The plea covers conduct by Weiner from January through March of a year ago, the person said. Weiner's brother was the only family in court to watch as he said he "hit bottom" and began therapy.
Weiner expected to plead guilty of sending obscene material to minor
The Daily Mail reported in September that Weiner had exchanged pictures and sexual messages with a 15-year-old girl. A message left with a representative for Abedin seeking comment Friday morning was not immediately returned.
David Schaefer, a spokesman for the law firm Covington & Burling, whose attorney, Arlo Devlin-Brown, is representing Weiner, said the former congressman's lawyer will comment later Friday. The allegations first surfaced in the Daily Mail.
In a statement to CNN at the time of the first reports, Weiner neither confirmed or denied sending the texts.
"I have repeatedly demonstrated bad judgment about the people I have communicated with online and the things I have sent".
His failed mayoral bid is the subject of the documentary "Weiner".
Federal prosecutors in NY said Weiner admitted to sending sexually explicit photos and "directions to engage in sexual conduct" to a 15-year-old girl.
The current investigation has been ongoing for several months and has had implications at the very top of United States politics - for it was during the current inquiry that the FBI found a number of emails directed to Abedin and subsequently reopened its review of Clinton's private email server, just 11 days before polling for the U.S. presidential election opened.
He surrendered to police this morning and appeared in court at 11am local time (4pm GMT), according to the Federal Bureau of Investigation. The source added the filing had been filed prior to Friday's hearing.