Daskin and Ozdemir are at the Turkish Embassy in Baghdad, and officials said they are expected to return to Turkey on Monday, Anatolian said.
Ali Daskin and Abdullah Ozdemir were seized while at work by an Iraqi resistance group who said last week the two men would be killed if their companies, Sa-Ra and Usluel, did not leave Iraq within 72 hours.
On Thursday, the firms said they were both pulling out.
"They treated us well. They gave us food and a place to sleep ... I'm thankful to be free," one of the men said in footage shown by the private CNN Turk television station.
Scores of foreign workers in Iraq have been seized since April. Many have been released but some have been killed.
The body of a slain Turkish truck driver was found on a roadside north of the town of Baiji on Friday. At least two other Turkish nationals have been killed by their captors.
Several Turkish firms have withdrawn from Iraq amid security concerns for their personnel.