Davutoglu posted the photo on his Instagram account.
"We link the continents not only with the third bridge, but also with our hearts,” Davutoglu said of the bridge, spanning Istanbul’s European and Asian sides.
The Yavuz Sultan Selim Bridge, the third in Turkey’s biggest metropolis, is scheduled to be operational this August.
On Sunday the final and middle section of the bridge was placed during a ceremony attended by Erdogan, Davutoglu, and Transportation Minister Binali Yildirim.
The bridge is named after 16th century Sultan Selim I, whose rule marked the expansion of Ottoman power in the Middle East.
When completed, the bridge, with a reported $3 billion price tag, will be 59 meters wide and 1,408 meters long.
The bridge will boast eight lanes for motor vehicles and two lanes for rail traffic.