0707 GMT May 28, 2018
Anies Baswedan and his supporters cheered as news came through that surveys showed him winning by over 10 percentage points against Basuki Tjahaja Purnama, who was fighting for his job while standing trial for blasphemy, AFP reported.
Official results are not expected until early May but the private pollsters, who count a sample of votes, are usually accurate.
Baswedan, a former education minister, thanked Jakarta's voters for supporting him and hinted that he would move to heal the divisions in the capital after the bitter poll, if his victory was confirmed.
"We celebrate diversity... We are all ready to work together again," the 47-year-old said.
Purnama, the city's first non-Muslim governor for half a century and its first ethnic Chinese leader, congratulated Baswedan and his running mate, adding: "We are all the same, we want a good Jakarta, because it is our home."
The governor – known by his nickname Ahok – lost a once-unassailable lead after a controversy erupted last year over charges that he had insulted Islam, a grave charge in Indonesia.
He is facing blasphemy charges for having recited a verse from the Holy Qur’an to accuse his opponents of using the holy book to turn voters against him in November 2016.
The move drew hundreds of thousands of Muslims onto the streets of Jakarta in major protests, and led to Purnama being put on trial for blasphemy.
Purnama has denied an intention to insult Muslims.
He won in the election's first round in February but Baswedan was seen as the favorite in the runoff because the votes from a third, Muslim candidate who was knocked out were expected to go to him.
Opinion polls in the run-up to the vote indicated that the race was neck and neck but in the event Baswedan strongly defeated Purnama, the pollsters indicated. They showed him with about 57 percent to Purnama on 43 percent.
More than 7.2 million people were registered to vote in the polls, which are also important as politicians view them as a potential stepping stone to the presidency in 2019.
Purnama's long-running blasphemy trial began in December. Prosecutors are due to recommend a sentence on Thursday, and a verdict is expected within weeks.
Many voters still supported Purnama due to his performance as governor since 2014. He had won praise for cleaning up once-filthy rivers and creating more green spaces, although his acerbic style had upset some.