And Weiner now faces a jail term of up to 27 months over his contact with the minor in 2016. Sentencing is scheduled for September 2017.
Based on the exchanges, Weiner allegedly knew she was only 15 years old.
The investigation infamously intersected previous year with the 2016 presidential campaign, when agents seized devices and found emails between Hillary Clinton and Huma Abedin, Weiner's estranged wife and a top Clinton adviser.
Weiner left Congress in June 2011 when sexually-charged, sometimes explicit, texts with women other than his wife first emerged.
Weiner, 52, stepped down from his congressional seat in 2011 over a sex scandal and was again exposed during his 2013 bid for NY mayor. A spokesperson with the Manhattan Supreme Court confirmed that Abedin, a close aide to Hillary Clinton, had filed court papers seeking a divorce.More news: Dozens dead after gunman torches Philippine casino
More news: US buildings light up green in solidarity with Paris climate accord
More news: Black Eyed Peas, Robbie Williams Added to Ariana Grande's Manchester Concert
The judge in Manhattan told Weiner he would have to register as a sex offender.
Weiner, who represented NY in Congress from 1999 to 2011, resigned after revelations that he was sending sexually explicit messages to multiple women.
The teen also said the two also had Skype conversations in which Weiner reportedly asked her about masturbation and requested she undress.
"These destructive impulses brought great devastation to my family and friends", Weiner said. "Anthony and I remain devoted to doing what is best for our son, who is the light of our life".
Weiner admitted to engaging in "obscene communications with this teenager, including sharing explicit images and encouraging her to engage in sexually explicit conduct", according to the newspaper.
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".
Clinton recently attributed her election loss in part to Comey's announcement. The failed mayoral bid is the subject of the documentary Weiner.