Unofficial tallies show that 61.45% voted in favour.
The military threw out the old constitution when it took power in 2014, after months of political instability and sporadic violence.
Supporters of the new document say it will restore stability, but critics say it will entrench military control.
Turnout was about 55%, the election commission said - well below its target figure of 80%.
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.
Independent observer groups had requested accreditation to monitor the vote, but this was not granted by the election commission.
But turnout was low, and the repressive climate which preceded the referendum, when campaigning against the charter was banned, will undermine the legitimacy of the result for many Thais.
The military now plans to hold a general election by the end of next year. Under the new voting system, this is likely to produce a weak coalition administration. And a wholly-appointed Senate and other unelected bodies will be given a decisive say over Thai politics, in what might best be described as a guided democracy.
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Guide me if old