"On behalf of the government of Georgia, as well as myself, I congratulate your Excellency on his victory in the presidential election," Kobakhidze said.
"I am confident that your efforts as the president of Iran will ensure a bright, stable and secure future for the country," he said.
"I wish health and success in government affairs to your Excellency and peace and prosperity to the people of Iran," he added.
Pezeshkian received more than 16 million votes against former nuclear negotiator Saeed Jalili with more than 13 million out of over 30 million votes cast, electoral authorities said.
"By gaining a majority of the votes cast on Friday, Pezeshkian has become Iran's next president," the interior ministry said.
The runoff on Friday followed a June 28 ballot in a snap election to find a successor to President Ebrahim Raeisi who lost his life with his foreign minister Hossein Amir-Abdollahian and others in a helicopter crash in northwest Iran.
Pezeshkian originally ran against a field of five candidates last week, winning the largest number of votes but falling short of a majority which sent him and Jalili to a second round.
MNA/