With more than 80% of contested seats now declared, Aung San Suu Kyi’s party has more than the two-thirds it needs to choose the president, ending decades of military-backed rule.
A quarter of seats are automatically held by the military, meaning it remains hugely influential.
Under the constitution Aung San Suu Kyi cannot become president herself.
Despite this, the election was seen as the first openly contested poll in Myanmar – also known as Burma – in 25 years.
By early Friday, the NLD needed two more votes to reach the threshold required for a majority.
Then at midday, the electoral commission said the party had taken 348 of the 664 seats in the two houses of parliament. This represents a two-thirds majority of the contested seats.
Votes are being counted and the final tally is not expected for several days.
The process of choosing Myanmar’s new president will begin in January, when parliament reconvenes.
Current President Thein Sein and the head of the military had already said they would respect the outcome and work with the new government.
They and the NLD are expected to being talks next week on the way forward.
About 30 million people were eligible to vote in the election – turnout was estimated at about 80%.
It was widely seen as a fair vote though there were reports of irregularities, and hundreds of thousands of people – including the Muslim Rohingya minority, who are not recognized as citizens – were denied voting rights.
The ruling military-backed Union Solidarity Development Party (USDP) – which won the last, widely criticized election five years ago – has so far gained about 5% of seats contested.
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