The US and European Union have welcomed the result of the Turkish constitutional referendum.
Voters in Turkey gave strong backing to a package of changes to the country's military-era constitution.
The changes are aimed at bringing Turkey more in line with the EU, which the government wants to join.
This result will help PM Recep Tayyip Erdogan, who made the reform a test of his leadership, ahead of elections next year, correspondents say.
With nearly all votes in the referendum counted, about 58% had voted "Yes" to amending the constitution.
Mr Erdogan said the result meant the country had "crossed a historic threshold toward advanced democracy and the supremacy of law".
The European Commission has welcomed the results.
"As we consistently said in the past months, these reforms are a step in the right direction as they address a number of long-standing priorities in Turkey's efforts towards fully complying with the accession criteria," Enlargement Commissioner Stefan Fuele said in a statement.
Mr Obama called Mr Erdogan to congratulate him.
The US president "acknowledged the vibrancy of Turkey's democracy as reflected in the turnout for the referendum that took place across Turkey today", a statement released by the White House said.
German Foreign Minister Guido Westerwelle said the vote was critical for Turkey's bid to join the European Union.
"This discussion in society, also about the concrete form of the balance of power in the state, is very much to be welcomed," Mr Westerwelle said in a statement.
The result gives a boost to Mr Erdogan's political standing, after a hard-fought campaign in which the main opposition accused him and his party, the AKP, which has its roots in political Islam, of trying to take control of the judiciary, says the BBC's Jonathan Head in Istanbul.
'Islamist coup'
Mr Erdogan and his Justice and Development Party (AKP) are now in a stronger position to seek a third term of office in the general election due in the middle of next year, our correspondent adds.
The AKP has clashed repeatedly with Turkey's highest courts, which see themselves as guardians of the country's secular values.
The opposition say two of the 26 planned amendments would give the government excessive influence over the judiciary.
They accuse the AKP of trying to seize control of the judiciary as part of a back-door Islamist coup.
In Istanbul - the most Westernised city in Turkey, where many are suspicious of the AKP's religious agenda - Ozgur Deniz voted "No".
"The bad thing about this referendum was that we had to either choose or reject the whole package," he told the BBC.
"This is a package where some things are good for democracy - such as less power for the military. But there are some items which might be used by the government to use democracy for non-democratic purposes, like the item regarding the judiciary," he said.
"This election shows the commitment of Turkish people to a more democratic Turkey, and the army has not got the same power as before," wrote Ahmet from Eskisehir in an e-mail to the BBC.
The Turkish President, Abdullah Gul, appealed for national unity. "From tomorrow onwards, Turkey needs to unite as one, and look ahead.
"The public has the final say in democracies. I would like to remind everyone to welcome the result with respect and maturity."
The present constitution was drawn up by a military junta which seized power in a coup exactly 30 years ago, on 12 September 1980.
In all, the reform package includes 26 amendments to the 1982 constitution, many of them backed by the EU.
Civilian courts will have the power to try military personnel for crimes against the state, while sacked military officers will have the right to appeal against their dismissal.
Gender equality will be strengthened, and discrimination against children, the old and disabled banned.
Workers will be allowed to join more than one union, and the ban on politically motivated strikes will be removed.
In parliament, elected lawmakers will be able to stay on if their party is disbanded by the court.
