Erdogan late Monday afternoon took the presidential oath of office to become the Republic of Turkey's first president under its new governmental system.
Mr Erdogan has largely ruled by fiat since 2016, when he imposed a state of emergency on the country in response to a failed coup attempt against him. The issue still polarises Turkey.
Opponents say the move marks a lurch to authoritarianism, accusing Erdogan of eroding the secular institutions set up by modern Turkey's founder, Mustafa Kemal Ataturk, and driving it further from Western values of democracy and free speech.
But the pro-government daily Yeni Safak wrote under the headline "historic day": "One page is closing in Turkish history and a new page is opening".
The president said the new system makes the marginalization, persecution, and alienation of people a thing of the past.
In one of the most significant changes, the European Union affairs ministry, set up in 2011 to oversee Turkey's faltering bid to join the bloc, will be subsumed into the foreign ministry.
Erdogan was elected on June 24 in a vote marking Turkey's transition to an executive presidential system of government, doing away with the prime minister's post, among other changes.
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Together with the officers and guests of the ceremony, some 10,000 people are expected to take part.
Maduro, who tweeted the praise as a video message, was among more than 50 high-level foreign leaders, including 22 heads of states, who attended Erdoğan's inauguration ceremony at the presidential complex in Ankara on July 9.
Sudan's President Omar al-Bashir is on the guest list as is Emir Sheikh Tamim bin Hamad Al-Thani of Qatar, Turkey's closest ally in the Middle East.
The presidential aide stated that Buhari in the telephone conversation with Erdogan said he looked forward to the strengthening of relations between Nigeria and Turkey.
Current Foreign Minister Mevlut Cavusoglu could, in theory, continue in his job but reports have said Erdogan may choose his spokesman, Ibrahim Kalin, or even spy chief Hakan Fidan to succeed him.
He won last month's election with 52.9 percent of the vote, ushered in the executive presidency that ends parliamentary governance and boosts the powers of the formerly ceremonial presidency.
The AKP failed to win a majority in parliament, taking 294 of the 600 seats, meaning it will need its allies in the Nationalist Movement Party (MHP), which has 49 seats, to ensure a majority.