A total of 51.6 per cent of Serbia's 6.6 million-strong electorate supported the constitution, said Zoran Lucic of the independent Centre for Free Elections and Democracy [CESID], which monitors polls throughout the former Yugoslavia.
"We can say with a fairly high level of reliability that the majority of voters have supported the constitution," Lucic told journalists in the capital Belgrade.
"This is not the final estimate, but it is highly reliable," he said, adding that the turnout in the two-day referendum was 53.5 per cent.
The referendum, which had to be approved by at least 50 per cent of Serbia's registered voters, passed by a slim margin of 94,000 votes, said CESID.
The document claims the disputed southern province of Kosovo as an "integral" part of Serbia.
The move is seen as an apparent bid to pre-empt UN-backed talks on the province's status, which are widely expected to lead to a form of independence by the year's end.
Separately, Serbia's state-run RTS television reported without naming its sources that up to 52 per cent of the electorate supported the new charter.
The vote passed without any major incidents, observers said earlier.
The new constitution was unanimously backed by the Serbian parliament on September 30, in a rare show of political unity.
The referendum on the charter was being held over two days in a bid to combat the low turnout that has plagued Serbian elections in recent years.