Describing the monumental change as a "new beginning", he vowed at a later ceremony at his vast Ankara presidential palace to be the president of all 81 million Turks.
Presidents of Bulgaria, Georgia, Macedonia, Moldova, Bosnia and Herzegovina, Serbia, Kosovo, Pakistan, Kyrgyzstan, Sudan, Guinea, Zambia, Guinea Bissau, Equatorial Guinea, Somalia, Mauritania, Gabon, Chad, Djibouti and Turkish Republic of Northern Cyprus, as well as Emir of Qatar, attended the inauguration.
Prime Minister Binali Yildirim now goes down in history as the 27th and final holder of the post in Turkey.
Secretary generals of Organization for Security and Cooperation in Europe (OSCE) and D-8, and European Commissioner for Migration and Home Affairs were also be among the attendees.
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.
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.
Erdogan took the oath of office on Monday in the Turkish parliament, where he vowed that he would make the right use of the sweeping powers he won in a referendum past year and sealed in a hard-fought re-election victory two weeks ago.
In a referendum previous year, Turkish voters approved a series of comprehensive changes that granted significantly more powers to the president, eliminated the prime minister position and increased the size of the country's parliament, to name a few. "We are leaving behind the system that has in the past cost our country a heavy price in political and economic chaos".
His supporters, however, insist Erdogan deserves to be empowered as president, saying he has steered Turkey through its years of economic progress while rewarding working classes in the country.
The post of prime minister has been scrapped and the president will be able to select a cabinet, regulate ministries and remove civil servants, all without parliamentary approval. Inflation surged last month above 15 percent, its highest level in more than a decade, even though the central bank has raised interest rates by 5 percentage points since April. However, major Western leaders would not be in attendance, according to Reuters.
Those changes concentrate more power in the hands of the president. "In other words, Turkey will be an institutionalized autocracy", former EU Ambassador to Turkey Marc Pierini said. Erdoĝan has repeatedly clashed with strategic allies such as the U.S. and the European Union in recent years over the war in Syria, Turkey's accession to the EU, human rights abuses by Ankara, Europe's failure to support Turkey during the coup attempt, and rising Islamophobia in Europe.
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".
Last month Mr Erdogan was re-elected with 53% of the vote.
Turkey also faces a widening current account deficit making it reliant on weak foreign investment to plug the gap.
Under the new system, the counting of terms starts afresh, which means he starts his first five-year term on Monday.