Amina Ali Nkeki, 19, was found with a baby by an army-backed vigilante group on Tuesday in the huge Sambisa Forest, close to the border with Cameroon.
She was one of 219 pupils missing since they were abducted from a secondary school in eastern Chibok in April 2014.
They were taken by the Islamist militant group Boko Haram.
Amina was reportedly recognised by a civilian fighter of the Civilian Joint Task Force (JTF), a vigilante group set up to help fight Boko Haram.
She was with a suspected Boko Haram fighter who is now in the Nigerian military's custody. Named as Mohammed Hayatu, he said he was Amina's husband.
Aboku Gaji, leader of the JTF in Chibok:
"The moment this girl was discovered by our vigilantes, she was brought to my house. I instantly recognised her, and insisted we should take her to her parents.
"When we arrived at the house... I asked the mother to come and identify someone. The moment she saw her, she shouted her name: 'Amina, Amina!' She gave her the biggest hug ever, as if they were going to roll on the ground, we had to stabilise them.
"The mother called the attention of other relations to come out and see what is happening. The girl started comforting the mother, saying: 'Please Mum, take it easy, relax. I never thought I would ever see you again, wipe your tears. God has made it possible for us to see each other again.'
"Afterwards, we had to make them understand that the girl would not be left in their care. She must be handed over to the authority."
Interview with BBC Hausa service
Amina and her baby have been taken to taken to the regional capital Maiduguri for medical attention, the military said.
A spokesman for Nigeria's President Muhammadu Buhari said the rescued young woman would be brought to meet the head of state, before being helped to reintegrate into society.
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Hosea Abana Tsambido, the chairman of the Chibok community in the capital, Abuja, told the BBC that Amina had been found after venturing into the forest to search for firewood.
"She was sayingâ€¦ all the Chibok girls are still there in the Sambisa except six of them that have already died."
By Will Ross, BBC News
Amina was found by a local vigilante group out on a routine patrol.
These groups, which have played a vital role in the fight against Boko Haram, sprang up in 2013 in the main city of north-east Nigeria, Maiduguri.
It was a desperate measure at a terrible time when the jihadists were winning the war, seizing territory whilst reports of soldiers fleeing rather than fighting were common.
More vigilante groups then sprang up across the north-east and, with local knowledge of the terrain, they had some success stopping their homes from being taken over - even though they were armed with just rudimentary weapons.
As the Nigerian military started getting its act together at the beginning of 2015, with help from outside, it started retaking territory and in some areas worked effectively with the vigilantes.
There is, however, great concern that as peace returns the vigilantes - who have tasted power - pose a danger themselves.
During the April 2014 attack, Boko Haram gunmen arrived in Chibok late at night, then raided the school dormitories and loaded 276 girls on to trucks.
More than 50 managed to escape within hours, mostly by jumping off the lorries and running off into roadside bushes.
A video broadcast by CNN in April this year appeared to show some of the kidnapped schoolgirls alive.
Fifteen girls in black robes were pictured. They said they were being treated well but wanted to be with their families.
The video was allegedly shot on Christmas Day 2015 and some of the girls were identified by their parents.
The Chibok schoolgirls, many of whom are Christian, had previously not been seen since May 2014, when Boko Haram released a video of about 130 of them gathered together reciting the Koran.
The abduction led to the #BringBackOurGirls campaign, which was supported by US First Lady Michelle Obama and Pakistani activist Malala Yousafzai.
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The first of the missing Nigerian schoolgirls to be rescued since her capture two years ago has had an emotional reunion with her mother.