The 52-year-old, wearing a dark suit and tie, broke down repeatedly, sobbing as he read out a statement attesting to his guilt in a Manhattan federal court.
Weiner, once a rising talent in the Democratic Party, admitted to sending explicit photographs and messages to a 15-year-old high school girl last year as his wife worked on Clinton's presidential campaign.
He surrendered to the FBI on Friday morning and was released on bail after agreeing to turn in his passport, limit his travel to New York and continue mental health treatment. He will also have to register as a sex offender.
"I am guilty your honor," he said. Speaking through tears, his voice cracking and his words at times inaudible, he apologized to all those he had hurt and for the "great devastation to family and friends."
"I knew it was morally wrong and unlawful," Weiner told the court, stopping to wipe his brow, sniff and sip water from a bottle.
"I have a sickness but I do not have an excuse," he said. "I apologize to everyone I have hurt."
He pleaded guilty to one count of transferring obscenity to a minor. The crime carries a maximum sentence of 10 years in prison. Federal prosecutors are seeking a jail term of 21-27 months for Weiner.
District Judge Loretta Preska said Weiner would have to meet a probation officer for a pre-sentencing report. As part of the plea deal, he also has to surrender an iPhone.
Weiner, who put up a $150,000 bond, is scheduled to be sentenced on September 8.
"Weiner's conduct was not only reprehensible, but a federal crime, one for which he is now convicted and will be sentenced," said acting Manhattan US Attorney Joon Kim.
The ex-lawmaker used online messaging and video chat applications to communicate knowingly with a teenager, sending her obscene material and directions to engage in sexual conduct, as well as sexually explicit images.
US media reported shortly after the guilty plea that wife Huma Abedin had filed for divorce.
She announced their separation in August after The New York Post published sexually suggestive photographs that he shared with a woman while his four-year-old son apparently slept nearby.
Weiner was forced to resign his seat in Congress in 2011 after a similar scandal in which he admitted to exchanging sexually explicit pictures and messages with at least six women. His wife stood by him at the time.
Late last year, he was caught up in Clinton's email scandal when hundreds of thousands of the former secretary of state's emails were apparently found on his laptop.
As a result the FBI effectively re-opened its probe just weeks before the presidential election, a fact that Clinton has said played a key role in her shock defeat to Donald Trump.