The release of the pair demonstrated Iran's influence with its ally Syria, which lost Turkey's friendship when it cracked down on pro-democracy protests that erupted last year. Iran and Syria, both isolated by the West, have stuck by each other.
The two journalists were flown to Tehran, where they told Turkey's Anatolian news agency they were in good health and looking forward to being reunited with their families.
In remarks on his Twitter account, Davutoğlu said the Turkish government was sending a plane to bring them home. His Iranian counterpart Ali Akbar Salehi had told him earlier that the journalists had been freed, he added.
Adem Özkose, 34, a reporter with Milat, a small Islamic-leaning startup newspaper, and freelance cameraman Hamit Coşkun, 21, went missing in early March after sneaking across the border into Idlib, a northwestern province that has been the focus of an offensive by Syrian President Bashar al-Assad's forces.
Hopes for their release soared after Turkish officials revealed on Thursday that Iran was acting as a go-between. It was not immediately clear who had been holding them.
Turkey has closed its embassy in Damascus and halted flights to and from Syria.
Assad belongs to the minority Alawite sect, an offshoot of Shi'ite Islam. Iran is mostly Shi'ite, while most Turks and Syrians are Sunni Muslims.
Some 23,000 registered Syrian refugees live in camps in Turkey along its border with Syria, and an estimated 2,000 more are staying with Turkish relatives.