Jigme Singye Wangchuck, the former king, decided to hand power to an elected government, against the will of many subjects, before passing his crown to his son last December.
The polls are designed to teach voters and officials about the election process, in a country moving slowly into the modern world.
The royal family and other officials urged citizens to come out in huge numbers to vote after only 51 per cent of registered voters turned out for last month's preliminary round.
Long queues were reported from most parts of the country as citizens set out from the early morning hours to cast their ballots.
Gopilal Acharya, the editor of a private newspaper, said: "It seems people are taking the final round seriously as there are people who have travelled for hundreds of kilometres to vote in their home towns.
"It is a slow, but sure march towards democracy."
But not everyone is happy.
Thousands of ethnic Nepalis expelled from Bhutan in the early 1990s have threatened to protest.
They want the right to return to their birthplace and take part in the democratic process.
The authorities have said they are on alert after a threat of bomb attacks by the Bhutan Tiger Force, the militant wing of the Bhutan Communist party.