The report said President Mahmoud Ahmadinejad congratulated Hasan Rowhani on his victory in the Friday election.
Rowhani won the election outright by gaining nearly 51 percent of the vote, eliminating the need for a runoff. He is considered relatively moderate, though he backs pursuing Iran's suspect nuclear development program.
Rowhani has pledged to work for better ties with the world, aiming to reduce the West's sanctions against Iran over the nuclear issue.
The West suspects Iran intends to build nuclear weapons. Iran denies the charge.
Ahmadinejad was demonstrably hostile to the West, and his frequent belligerent statements were seen as worsening the already tense relations between Iran and the world.
At the meeting between the outgoing and incoming presidents, Ahmadinejad said his administration "is ready to transfer all responsibilities to the next government in a proper way," according to the report.
Rowhani said, "The transitional period requires cooperation and coordination, and all parties are ready for this." He said they appointed a two-member committee to follow up on their talks.
Rowhani said the country can promote welfare and global progress by "respecting differences." He is set to take office in August.
The meeting took place in Rowhani's office in Tehran, in a building said to have been designed by Mir Hosein Mousavi, the main reformist challenger of Ahmadinejad in his disputed 2009 re-election, which set off protests and street riots by reformers who alleged that the election of Ahmadinejad was fraudulent. The government cracked down hard on the protests and the reform movement.
Mousavi and his fellow pro-reform leader, Mahdi Karroubi, have been under house arrest for more than two years.