This is the first visit of Abdul-Mahdi to Tehran which follows the official invitation of Rouhani, who had paid a five-day visit to Baghdad in March.
Heading a high-ranking politico-economic delegation, Abdul-Mahdi is scheduled to hold separate talks with senior governmental figures, including Foreign Minister Mohammad Javad Zarif.
The Iraqi official will also take part in the third Iran-Iraq economic forum, which will be attended by a number of businesspersons of the two neighboring countries.
On the second day of his trip, he will make a visit to the holy shrine of Imam Reza (PBUH), the eighth Shia Imam, in the northeastern city of Mashhad.