His move comes after reports of a deepening rift with President Recep Tayyip Erdogan.
At a press conference following a meeting of the AKP leadership in Ankara, Davutoglu said he had taken the step after “consultations with our president and those whose views I trust.”
He called an extraordinary party congress on May 22, when he will formally step aside and his successor will be considered.
Davutoglu, who became prime minister in 2014, is currently the chairman of the conservative AKP party, which has ruled Turkey since 2002.
By stepping aside, analysts say Davutoglu would effectively be allowing Erdogan to choose a new party boss – someone who would then go on to be named prime minister.
The political drama comes as: Turkey hosts 2.2 million refugees from the Syrian war; the government battles with Kurdish fighters in the restive south-east; and security worries mount after a series of recent terrorist attacks have left dozens dead.
Investors were rattled Thursday by the uncertainty, with the yield on 10-year government bonds rising 37 basis points to 10 per cent – the highest one-day increase since June 2015.
On the stock market, the leading ISE National 100 index was experiencing its fifth straight day of declines.
Davutoglu had been hand-picked by Erdogan to become the party leader and was the sole candidate on the ballot when he was elected to the position by AKP members in 2014.
But disagreements between the low-key Davutoglu, known for his pragmatic approach, and the more confrontational Erdogan, have emerged on issues ranging from closer relations with the European Union to the conflict with Kurdish separatists.
Davutoglu’s power to appoint local party leaders has also been recently curtailed, reports said.
Transport Minister Binali Yildirim and Energy Minister Berat Albayrak, who is Erdogan’s son-in-law, are among those being considered as possible successors, according to the Cumhuriyet daily.
Erdogan, whose rule has become increasingly authoritarian, is pushing for a new constitution to replace the current document, which was drafted after the 1980 military coup.
He argues the rewriting the document will help the country function more smoothly. Critics say it is a move to give more authority to the presidency and allow Erdogan, who was prime minister for more than a decade before becoming president, to tighten his grip on power even further.
But to put a new constitution to a popular referendum, the AKP would need at least 330 votes in parliament. The Islam-rooted party, founded by Erdogan, currently commands 317 seats in the 550-member house.
Born in 1959, Davutoglu received a doctorate in international relations from Turkey’s Bogazici University and worked for years as a professor before becoming foreign minister in 2009.