The port, located in Iran's southeastern Sistan-Baluchistan province, was inaugurated by Rouhani in the presence of representatives from India, Afghanistan and several other countries of the region, Indian Times reported.
The first phase of the Chabahar port project is known as the Shahid Beheshti port, according to the report.
Iran is believed to have asked the Indian government to "manage" or operate the first phase of the port until work for the second phase is finalized, the report said.
It said that ahead of the inauguration, India’s External Affairs Minister Sushma Swaraj and her Iranian counterpart Javed Zarif, held a meeting in Tehran on Saturday to review the implementation of the Chabahar port project, among other issues.
The report added that Zarif had referred to the Shahid Beheshti Port and said it reinforces mutual and regional cooperation between India and Iran.
"It also shows the importance of the port in the development of the region and the routes that connect Central Asian states to other countries in the world through the Sea of Oman and the Indian Ocean," he said, according to the Iranian Foreign Ministry.
Over a month ago, India had sent its first consignment of wheat to Afghanistan by sea through the Chabahar port in Iran.
"The shipment of wheat is a landmark moment as it will pave the way for operationalization of the Chabahar port as an alternate, reliable and robust connectivity for Afghanistan," the ministry of external affairs (MEA) had said in a statement.
Besides the bilateral pact to develop the Chabahar port, for which India will invest $500 million, a trilateral Agreement on Transport and Transit Corridor has also been signed by India, Afghanistan and Iran.