Official results will not be released until January 2, although similar polls - known as "quick counts" - accurately forecast the result of national elections in Indonesia in 2004 and in scores of other countries in the world.
The polls are the first since the government and separatists signed a peace deal in the province last year.
The vote comes almost two years after the Asian tsunami which killed an estimated 167,000 people in Aceh alone.
The huge loss of life proved the eventual spur to bringing an end to the province’s brutal 29-year civil war.
In a Finnish-brokered peace deal signed on August 15, 2005, both the rebels and the Indonesian government made major concessions.
The separatist Free Aceh Movement (GAM) gave up its long-standing demand for complete independence and agreed to disarm itself.
Post-tsunami rehousing: Some 25,000 families homeless
Disputes about dividing government funds for reintegration of former rebels
Tackling unemployment among demobilised rebels
Overseeing Islamic sharia courts and authority of religious police
Meanwhile the government removed half of the 50,000 troops stationed in Aceh and promised the region control of 70 per cent of it mineral wealth.
A force of 13,000 police officers was deployed to monitor voting at more than 8,400 polling stations.
There were no reports of poll violence, but police said unknown perpetrators detonated a small bomb inside a partially constructed school at dawn in northern Aceh. There were no injuries.