The president will sit at the top of a vertical power structure marked by a slimmed-down government with 16 ministries instead of 26 and multiple bodies reporting to him.
After the swearing-in ceremony, Mr Erdogan visited the mausoleum of the founder of the Turkish Republic, Mustafa Kemal Ataturk before proceeding to the Presidential Complex to make his inaugural speech.
Parliament can ratify or reject his budget and the president needs parliamentary approval for emergency rule and decrees passed during that time. The introduction of the new presidential system marks the biggest overhaul of governance since the Turkish republic was established on the ruins of the Ottoman Empire almost a century ago.
Erdogan previously said that there will not be any members or parliamentarians of his Justice and Development Party (AK Party) in the new cabinet, hinting that it will be made up of ex-politicians and bureaucrats.
Erdogan will face immediate and major challenges in his second term, posed by an imbalanced fast-growing economy and foreign policy tensions between the West and Turkey, a North Atlantic Treaty Organisation member.
Russian Prime Minister Dmitry Medvedev was present, in a new sign of the warm ties between Ankara and Moscow, as was Venezuelan President Nicolas Maduro, regarded with disdain by Washington but an ally of Erdogan. Under controversial constitutional reforms approved by a referendum previous year, parliament has been weakened and the post of prime minister abolished.
Turkey's Tayyip Erdogan fulfilled a long-held ambition on Monday when he was sworn in as president with sweeping new powers over a country he has dominated and reshaped during his 15-year rule.
Raheem Sterling thanks England fans after reaching ‘dream’ World Cup semi-final
He would have knocked that one in over the top, he's got a great touch. "If we had England's money, who knows where we'd be in our country?"
Prime Minister Binali Yildirim now goes down in history as the 27th and final holder of the post in Turkey.
The lira on Tuesday gained back 0.5 percent against the dollar to trade at 4.7 to the greenback.
The lira has been battered by concern about Erdogan's drive for lower interest rates and by comments in May that he planned to take greater control of the economy after the election, which he won on June 24.
"We are leaving behind the system that has in the past cost our country a heavy price in political and economic chaos", Erdogan said in an address late on Monday. But he's also overseen a strong economy and he has built up considerable support across the country. "In other words, Turkey will be an institutionalized autocracy", former EU Ambassador to Turkey Marc Pierini said.
In the aftermath of the 2016 coup, Turkey, a member of the North Atlantic Treaty Organisation military alliance and still nominally a candidate to join the European Union, has detained some 160,000 people, jailed journalists and shut down dozens of media outlets.
Investors are also keen for details on Erdogan's new economic team, which is expected to be announced later on Monday.
"For the cabinet appointments in the past several years, the most important issue has been the presence of the current deputy prime minister, Mehmet Simsek", said Inan Demir, a senior economist at Nomura International.