Amina Ali with her baby.
Amina Ali was discovered on Tuesday in the Sambisa Forest area of Borno state, and was brought back to her home town of Mbalala, near Chibok.
The head of the Abducted Chibok Girls Parents' group, Yakubu Nkeki, said the teenager who was 17 when she was abducted, was brought to his house where she was reunited with her mother.
"When her mother approached the car the girl stepped out and her mother exclaimed, 'Amina! Is that you?'," local community leader Ayuba Alamson Chibok said.
"They ran towards each other and hugged. The mother burst into tears."
Soldiers working together with a civilian vigilante group rescued the teenage girl and her four-month-old baby in the remote north-east of Nigeria, army spokesman Sani Usman said.
They also detained a "suspected Boko Haram terrorist" called Mohammed Hayatu who claimed to be the girl's husband, Mr Usman added.
"Preliminary investigation shows that she is indeed one of the abducted Chibok schoolgirls abducted by Boko Haram terrorists on 14th April 2014 in Chibok," Mr Usman said in a statement.
Activists quoted her saying that her schoolmates were still in the Sambisa Forest, Boko Haram's biggest stronghold.
Community leader Hoses Tsambido also quoted her as saying that "six were already dead".
Boko Haram captured a total of 276 girls from their school in Chibok in April 2014 as part of a seven-year insurgency to set up an Islamic state in the north which has killed some 15,000 people and displaced more than 2 million.
Dozens of the girls escaped in the initial melee in 2014 but 218 remained unaccounted for.
Nothing had been heard from the 219 since a video published by the Islamists in May 2014, until an apparent "proof of life" message was sent to the Nigerian Government earlier this year.
Parents had accused former president Goodluck Jonathan, Nigeria's leader at the time of the mass kidnap, of not doing enough to track them down and bring them home.
Other abducted girls 'heavily guarded' in Sambisa ForestAli's rescue should give a boost to President Muhammadu Buhari, a former military ruler who had made crushing the Boko Haram insurgency a central pillar of his presidential campaign in 2015.
Activists at #Bringbackourgirls, which have been campaigning for the girls' release, confirmed Ms Ali's release.
Mr Tsambido confirmed the discovery but did not provide details.
"Her name is Amina Ali Darsha. She was found yesterday in an area of Kulakasha at the fringes of Sambisa Forest," he said.
"Right now she is with the military in Damboa."
Mr Usman said Ms Ali and her alleged husband had been brought to the state capital, Maiduguri, "for further medical attention and screening".