Her party, the National League for Democracy, is expected to win by a landslide, taking 154 of the 164 seats in four states where results have been counted.
There has been no official result yet in Myanmar's first openly contested elections in 25 years, but it seems to be great news for Aung San Suu Kyi.
Early results indicate her National League for Democracy party is on course for an emphatic victory.
The NLD says its own tally indicates up to 75 per cent of Myanmar's parliamentary seats should be going their way.
The ruling Union Solidarity for Development Party (USDP), created by the former military government and led by retired officers, has already conceded defeat.
However there are concerns whether the military will remain true to its word.
In the 1990 general election, the NLD won 59 per cent of the national votes and 392 of the 485 seats in Parliament, but the country's military rulers refused to accept the result.
They had detained Aung San Suu Kyi under house arrest before the elections, where she remained, on and off, until her most recent release on 13 November 2010.
Ms Suu Kyi believes this result will be accepted and voters will no longer tolerate any unnecessary military intervention.
"Whether it's the military or any other body, collaboration and cooperation is something you have to work at. It doesn't happen overnight. You have to learn to build it up by working, not just in a theoretical way. So how we deal with the situation depends on how the situation evolves. It's not something you can set hard and fast rules for."
Even if the NLD can form the country's first democratically elected government since the 1960s, it will face major hurdles.
The new government won't take power until February, which means the current government can continue to make laws.
Then there is the constitutional ban which bars Ms Suu Kyi from becoming president.
But the Nobel peace laureate has described her new role as "above the president":
"I make all the decisions because I'm the leader of the winning party and the president will be one whom we will choose just in order to meet the requirements of the constitution. That is the only logical way to do it, because in any democratic country it's the leader of the winning party who becomes the leader of the government and if this constitution doesn't allow it, then we'll have to make arrangements so that we can proceed along usual democratic lines."
Dr Melissa Crouch is from the University of New South Wales Law School and is in Yangon.
She has told the ABC despite the optimism sweeping across Myanmar, there are tough times ahead for Ms Suu Kyi.
"One of the things going forward for her I think is how to will form a judicial system in particular, as well as dealing with a parliament that still has 25 per cent of the fixed reserves for the military. As well as a smaller number of ethnic groups, political parties, that she will have to work with."
Among those groups are the Muslim Rohingya people, who are struggling for recognition of their identity in their home in Myanmar's Rakhine state.
Ms Suu Kyi says the NLD is excited to work with all concerned to make Myanmar a truly democratic nation.
"We cannot be an authoritarian government for the simple reason, because our strength is the people, it's the public. We have been able to survive as long as we have because we have the support of the people and governments that depend on the support of the people will never become authoritarian."
Meanwhile, European Union observers say last Sunday's vote went "better than expected", but more reforms are needed to ensure genuine elections in the future.
EU chief observer Alexander Graf Lambsdorff has praised Myanmar on a smooth voting process.
"As far as the voting process and the polling stations are concerned, 95% of the ratings that we obtained were a 'good' or a 'very good'. That is a very high number."
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