Election board chairman Sadi Guven said the poll would be held on 1 November.
Part of Mr Davutoglu's job will be to oversee the elections. He has five days to form a cabinet.
The constitution says all parties should be represented in the interim administration but this is the first time such a government has been needed and the leader of Turkey's pro-Kurdish opposition said he would not be surprised if Mr Erdogan tried to exclude it.
Kurdish Peoples' Democratic Party (HDP) leader Selahattin Demirtas said it would be prepared to take part, although the main opposition Republican People's Party (CHP) and Nationalist Movement Party (MHP) have refused to do so.
The CHP, which came second in June's vote, had asked for a mandate to try to form a new government.
But the president instead opted for a re-run of the elections.
Mr Erdogan, who founded the AK Party in 2001, previously denied allegations that he had undermined the coalition talks in order to force a new vote.
June's result appeared to block his plans to boost the powers of the presidency in Turkey.
In the new election, the AKP will need 60% of seats to be able to call a referendum on presidential powers. With a two-thirds majority it could change them without a referendum.
But the AKP only secured 41% at the polls in June.
The political uncertainty comes amid rising violence in Turkey and neighbouring Iraq and Syria.
An uneasy two-year ceasefire with the outlawed Kurdistan Workers Party (PKK) fell apart last month, after a suicide bomb blamed on the so-called Islamic State killed 32 young activists in the largely Kurdish city of Suruc, close to the Syrian border.
In recent weeks Turkish forces have carried out attacks on militants from IS in Syria and have bombed Kurdish PKK camps mainly in northern Iraq.
The army said on Tuesday it had carried out further strikes against PKK bases in northern Iraq, killing 34 PKK members.
