Three hours before polling stations closed at 8pm (1600 GMT) on Sunday, the central electoral commission said the turnout had exceeded 44%, more than the participation of a third of voters necessary to validate the poll.
First results, based on 22% of Armenia's 1922 polling stations, showed 93.3% of ballots were cast in favour of the reforms, with only 5.3% objecting, the commission announced overnight.
Although few are against the proposed constitutional reforms, their adoption had been uncertain because the opposition had called for a boycott of the referendum as it views the government as illegitimate.
The opposition challenged the turnout figures and an hour before voting ended about 1000 opposition supporters gathered in the centre of the capital, Yerevan, to demonstrate.
Armenia's 2.3 million voters were asked to approve or reject the reforms which would also increase the powers of parliament and the government, strengthen judicial independence and allow millions of diaspora Armenians to obtain citizenship by scrapping a ban on dual citizenship.
The reforms were drafted with the assistance of experts from the Council of Europe, of which Armenia is a member, and the body called on voters to approve them.
The reforms are part of Armenia's commitments before the council, which could take disciplinary measures against Armenia if the vote fails, as it did two years ago when a similar referendum was declared invalid because of low turnout.
The reforms will curb President
Robert Kocharian's powers
President Robert Kocharian voted during the morning at a school in Yerevan but refused to predict the outcome, although he seemed to suggest that he would not mind if voters rejected the proposed reform.
"Today the people of Armenia face a choice," he said.
"I don't want to predict the outcome. But if the constitutional amendment does not pass, this means we will retain strong presidential power, and President Kocharian will continue doing what he's been doing."
Rene van der Linden, the head of the council's Parliamentary Assembly, said: "This [referendum] is an occasion for Armenians to show their commitment to Europe."
Opposition cries foul
Kocharian first came to power in 1998 and was re-elected in 2003 in a vote that many observers said was marred by fraud.
On Sunday, Viktor Dallakian, head of the opposition Unity bloc in the Armenian parliament, said: "We are watching the voting process and are seeing many violations.
"Our observers have already registered violations, for example some people are continuing to campaign at the entrances to polling stations and officials at bureaus are themselves putting voting slips in urns"
opposition Unity bloc chief
"Our observers have already registered violations, for example some people are continuing to campaign at the entrances to polling stations and officials at bureaus are themselves putting voting slips in urns."
He also claimed that the government was inflating the turnout figures.
"We say the turnout at 2pm was 5-6%, while the electoral commission says it was more than 26%."