Thais handed the junta of Prime Minister Prayuth Chan-ocha a convincing win in the referendum on Sunday, with preliminary results showing over 61 per cent voted in favour.
The full results are due on Wednesday.
Campaigning against the draft in the run-up to the referendum was banned and dozens of people were detained. Thailand's biggest political parties rejected the constitution.
About 200,000 police officers were deployed to maintain order and there were no reports of protests.
Thai officials immediately said that a democratically elected government will now take power in Thailand, at the earliest by December 2017.
But Fraser Cameron, director of the EU/Asia Centre in Brussels has dismissed the outcome of the much-awaited referendum.
Speaking to this website, Cameron said, “Flaws in the draft constitution mean that the referendum is unlikely to resolve the political crisis.”
Senior MEPs, including David Martin, a Scottish Socialist, and Tory deputy Charles Tannock had also voiced reservations about the constitution.
A desire to see greater political stability drove the yes vote, analysts said. Thailand has been rocked by more than a decade of political turmoil that has stunted growth, two military takeovers and several rounds of often deadly street protests.
"We think there will be an election at the earliest in September or October 2017 and a new government by December 2017," Chatchai Na Chiang Mai, spokesperson for the Constitution Drafting Committee, told Reuters.
Prior to Sunday’s vote, Thailand's major political parties had criticised the draft constitution, saying it would constrict democracy, including one provision calling for an appointed Senate with seats reserved for military commanders.
The 50 million eligible voters were asked to answer yes or no to the question: Do you accept the draft constitution? They were also asked a supplementary question, whether or not the appointed Senate should be allowed to join the lower house in selecting a Prime Minister.
Thailand has had more than a decade of fractured politics and instability that has sometimes spilled over into violence.
In this time, parties linked to former Prime Minister Thaksin Shinawatra have won every election, but their governments have all been ousted either by court rulings or military coups.
Thaksin fled into self-imposed exile in 2008 to escape a criminal charge of abusing his power, for which he was later convicted in absentia.
Speaking to this website last week, Willy Fautre, director of the Brussels-based NGO, Human Rights Without Frontiers, said, “The referendum under military control is a farce and there is no guarantee that it will be fair.
“It is just meant to boost military power as it extends too much power to the unelected NCPO, including the possibility of appointing an unelected military-backed Prime Minister.”