Indonesia's northwestern Aceh province has elected a former separatist leader as governor in a vote that marked another major step towards peace with the Free Aceh Movement (GAM).

Zaini Abdullah, an ex-foreign minister of the three-decades-old separatist group, won 55.8 per cent of the vote in last week's election, beating former governor Irwandi Yusuf, according to results announced by the Aceh independent election commission.

"Aceh has been so far an overwhelmingly successful example of resolving a guerilla conflict through allowing the rebels to take part in the political process," said security analyst Sidney Jones of the Brussels-based International Crisis Group.

Around 13 people died in the run-up to the election, according to Concord Consulting group, a risk firm based in Jakarta. There were also allegations of voter intimidation.

Even so, Aceh's second election forms part of a transition away from violence, according to analysts.

Abdullah worked as a doctor from 1972-1976 before joining the GAM and fighting for four years in the movement that sought independence for the region. He later sought asylum in Sweden where he represented the group as foreign minister before returning to Aceh in 2006.

Aceh is the only Indonesian province that has Sharia law, though the subject played little role in the election. Abdullah said that Sharia must be applied more evenly.

"On the bylaw about cutting the hands for stealing, you can cut two, three, twenty, thirty hands, but that will not resolve the problem. There should be a preventive action as well through education," Abdullah, 71, told Reuters.