The formal reason for Mr Erdogan's candidacy is that he is barred from standing again as prime minister by his own party's charter.
He says that if he wins, he wants to change the constitution to turn the largely ceremonial post of president into the country's executive powerhouse.
A US-style strong presidency, he argues, would suit Turkey more than its current parliamentary system.
Ruling party officials argue the presidency will have greater clout as it will now be decided by voters rather than parliament, as was previously the case.
The president already has the power to appoint the prime minister - subject to approval by parliament - and the army chief. He can also summon parliament and call referendums on constitutional changes agreed by MPs.