Mousavi stressed the readiness of the Army of the Islamic Republic of Iran to interact with Pezeshkian's administration.
He also wished Pezeshkian success on his mission to serve the Iranian nation.
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.
MP/6159623