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Mr Erdogan, who served three terms as PM, has vowed to give more power to the previously ceremonial post.
Critics of Mr Erdogan say the move will make him more authoritarian. Opposition MPs walked out of the ceremony.
Outgoing Foreign Minister Ahmet Davutoglu is set to be PM after being elected head of the governing AK Party.
Mr Erdogan promised in his presidential oath to protect Turkey's independence and integrity, to honour the constitution and adhere to the principles of the founder of modern Turkey, Mustafa Kemal Ataturk.
"In my capacity as president of the Republic, I swear upon my honour and repute before the great Turkish nation and before history to safeguard the existence and independence of the state," Mr Erdogan said at the brief ceremony in parliament.
The new president left parliament to lay a wreath at Ataturk's mausoleum in the centre of Ankara - widely regarded as one of the most important symbols of the secular republic.
Another ceremony was held at the presidential palace.
Following the inauguration, police used water canon to disperse about 200 protesters shouting slogans against Mr Erdogan in Turkey's biggest city, Istanbul.
Some carried banners saying "Presidency cannot wash away corruption or theft".