Relations between Ankara and Baghdad, which had been on the upswing as recently as 2011, fell off as the two countries clashed over the war in Syria, Turkey's ties with Iraq's autonomous Kurdish region, and sharp words between their prime ministers.
But the two sides have made moves in recent weeks towards a gradual rapprochement, with Turkish officials pegging Davutoglu's visit as focused on promoting a "fresh start", as well as concentrating on the violence in their common neighbor Syria.
The two-day visit, which follows a similar trip by Davutoglu's counterpart Hoshyar Zebari last month, includes talks with Prime Minister Nuri al-Maliki and Zebari, as well as several other officials and political leaders in Baghdad and the Shia holy cities of Najaf and Karbala.
"They are going to discuss a fresh start to relations," a Turkish official told AFP, speaking on condition of anonymity.
"They will mostly discuss bilateral issues, what is happening in the region, and Syria."
Ties between Iraq and Turkey had been rapidly improving in the run-up to the Syrian conflict, with multiple visits to Baghdad by both Davutoglu and Turkish Prime Minister Recep Tayyip Erdogan.
But disagreements over how to deal with Syria -- Turkey has backed opposition groups, while Iraq has said it is neutral -- were followed by Ankara's decision in early 2012 to give refuge to former Iraqi vice president Tareq al-Hashemi, convicted in absentia of organizing death squads.
They have accused each other of inciting sectarian tensions and, at various stages, summoned each other's ambassadors in tit-for-tat manoeuvers.
Baghdad has also slammed mooted energy deals between Ankara and the Kurdish region in northern Iraq.
"This marks a resumption of normal relations, and an end to tensions," Maliki's spokesman Ali al-Mussawi said before Davutoglu's arrival. "We hope relations will return to their normal state."
"The two countries have joint interests, history and challenges," he continued.
"Warm relations do not mean agreeing on all regional issues ... On those that we have differences, we will talk about them and solve them through dialog."
HH/HH