The election is a closely fought contest between two parties -- the People's Democratic Party and the Druk Phuensum Tshogpa.
The Oxford-educated King Jigme Khesar Namgyel is expected to retain a strong influence over how the country is run even after the assembly is elected.
PDP leader Sangay Ngedup is a former two-time prime minister in the old royal regime and is the brother of the four sisters and queens who are married to former king Jigme Singye Wangchuk.
DPT leader Jigmi Thinley is also a former premier and close to the country's educated elite.
Over 2.3 lakh of the 3.18 lakh voters cast their ballot in the election, which according to initial estimates, indicated a turnout of 72.33 per cent, Election Commissioner Deki Pema told PTI.
"Pagli Samste had the highest voter turnout of 86.79 per cent while Chhummey Ura had a low of 31.22 per cent," Pema said.
The positive response was not because the people were fed up with the monarchy, but due to the fact that their king wanted a change in the country, where development is measured by a strange index called 'gross national happiness', and they had to oblige him.
The polls were also reported to have been peaceful despite Nepal-based Maoist rebels threatening to disrupt the process.
"We have no reports of violence during the elections, not even from the sensitive areas," said Lt Col Chimmi Dorji of the Royal Bhutan Police who is also the security coordinator for the polls.
"We had adequate security personnel manning stations and border areas of the country," Dorji said.
From the morning itself there was a festive mood in the capital as people, wearing traditional ghos and kiras, were seen queuing up in polling stations to cast their vote as polling began at 9 am local time.
International observers, monitoring the polls, expressed happiness over the smooth conduct.
"The polls are being held in an orderly manner and the turnout is appreciative," said Ted Osius, US' political minister counselor.
"The elections have been well organised and the Election Commission of Bhutan should be lauded," Osius told PTI.
"The whole process has been well-planned and it is great to see the eagerness of the voters to come out and vote," said Pushpinder Dhillon, first secretary in the US Embassy in New Delhi.
A UN observer said Bhutan's transition to democracy will be smooth going by the progress of the political process it has adopted. A total of 865 polling stations were set up across the country that has 3,18,465 registered voters.
Bhutan's transition to democracy actually began in 2001 when former king Jigme Singye Wangchuk handed over the powers of daily governance to a Council of Ministers.
In 2006, he abdicated the throne in favour of his Oxford-educated son Jigme Khesar Namgyel.
In the run-up to the national assembly polls, two rounds of dummy elections were held last April and May in which the Bhutanese voted for traditional values.
Bhutan elected 15 members to its National Council or Upper House of Parliament on December 31, 2007, and five others on January 29. The king will appoint five more members to the apolitical council.
Image: Bhutanese citizens queue to cast their vote at a polling station in Zulukha, near Thimphu, on Monday.
Photograph: Deshakalyan Chowdhury/AFP/Getty Images