Turkish President Recep Tayyip Erdogan is taking on extensive new executive powers following his outright election victory in Sunday's poll.
Parliament has been weakened and the post of prime minister abolished, as measures approved in a controversial referendum last year take effect.
Defeated opposition candidate Muharrem Ince said Turkey was now entering a dangerous period of "one-man rule".
Mr Erdogan polled nearly 53% in the most fiercely fought election in years.
Mr Ince received just 31%, despite a lively campaign attracting huge crowds.
Mr Erdogan has presided over a strong economy and built up a solid support base by investing in healthcare, education and infrastructure.
But the 64-year-old has also polarised opinion, cracking down on opponents and putting some 160,000 people in jail.
Congratulations have come in from around the world, though some Western leaders have been slow to react. Russian President Vladimir Putin talked of Mr Erdogan's "great political authority and mass support".
In his victory speech to supporters early on Monday morning, Mr Erdogan vowed to bring the new presidential system into being "rapidly".
The constitutional changes were endorsed in a tight referendum last year by 51% of voters.
They include giving the president new powers to:
Supporters of Erdogan and the AK Party took to Istanbul's streets to celebrate
Some critics argue that Turkey's new system lacks the checks and balances of other executive presidencies like France or the US.
Mr Erdogan maintains his increased authority will empower him to address Turkey's economic woes and defeat Kurdish rebels in the country's south-east.
Mr Erdogan was prime minister for 11 years before becoming president in 2014. Under the new constitution, he could stand for a third term when his second finishes in 2023, meaning he could potentially hold power until 2028.
By Mark Lowen, BBC Turkey correspondent
Despite 90% of the media being pro-government and largely shunning the opposition, the president's posters and flags dwarfing any challenge on the streets, the election being held under a state of emergency curtailing protests, and critical journalists and academics being jailed or forced into exile, Mr Erdogan only got half of the country behind him.
"We are living through a fascist regime", the opposition MP Selin Sayek Boke told the BBC. "But fascist regimes don't usually win elections with 53%, they win with 90%. So this shows that progressive values are still here and can rise up."
For now, though, this is Mr Erdogan's time. With his sweeping new powers, scrapping the post of prime minister and able to choose ministers and most senior judges, he becomes Turkey's most powerful leader since its founding father Ataturk.
He'll now hope to lead the country at least until 2023, a hundred years since Ataturk's creation. And a dejected opposition will have to pick itself up and wonder again if, and how, he can be beaten.
Mr Ince, from the Republican People's Party (CHP), said the election was unfair from its declaration to the announcement of the results.
"The new regime that takes effect from today is a major danger for Turkey... We have now fully adopted a regime of one-man rule," he told journalists at a post-election news conference.
But he said that there was no significant difference between official results and his party's figures, and therefore he would accept the outcome.
There were another four candidates on the presidential ballot, all of whom fell below 10% of the vote.
Security was tight at polling stations. Ahead of the vote, concerns had been raised about potential voter intimidation and electoral fraud.
Voter turnout was high at almost 87%, the state broadcaster reported.
Rights activists have said the press is not free to report on all sides in Turkey. It has become the world's biggest jailer of journalists under Mr Erdogan's rule, according to monitoring groups.
Mr Erdogan has already cautioned his rivals against claiming foul play, saying: "I hope nobody will try to cast a shadow on the results and harm democracy in order to hide their own failure."
In separate parliamentary elections, the governing alliance led by Mr Erdogan's AK Party (AKP) secured a majority, with 53% and about 343 seats.
The opposition CHP and its allies won only 33% (190 seats). However, the pro-Kurdish HDP re-entered parliament with 67 seats.
Kurds in Diyarbakir celebrated the HDP's result
The party's success comes despite the fact its presidential candidate Selahattin Demirtas is in a high-security prison on terror charges, which he firmly denies.
The biggest issue for voters was the economy. The Turkish lira has tanked and inflation stands at about 11%, though the economy has grown substantially in recent years.
The currency has suffered as Mr Erdogan has pressed the central bank not to raise interest rates and suggested before the poll that he might restrict its independence.
Terrorism was another key issue, as Turkey faces attacks from Kurdish militants and the jihadists of the Islamic State group.
Mr Erdogan's rivals accused him of damaging civil liberties in Turkey and spearheading a slide into authoritarian rule.
Turkey has been under a state of emergency since a failed coup in July 2016, with 107,000 public servants and soldiers dismissed from their jobs. More than 50,000 people have been imprisoned pending trial since the uprising.