"I have arrived in Iran, a country with which we have linked civilisations. I hope to strengthen economic cooperation between the two countries," Modi wrote in a tweet sent in Farsi.
Iranian media reported that on Monday he will meet both President Hassan Rouhani and the Islamic republic's supreme leader Ayatollah Ali Khamenei during his two-day visit.
Modi's trip is aimed primarily at increasing economic and commercial ties with Iran.
Iran was India’s second largest supplier of oil until 2011-12, when economic sanctions against Tehran over its nuclear programme forced New Delhi to reduce its dependence on Iranian oil.
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According to Iranian media reports, India is now seeking to double its imports of Iranian oil.
The official IRNA news agency reported that Afghan President Ashraf Ghani would also be in the country on Monday to sign a tripartite agreement.
This would transform Iran's southern port of Chabahar on the Gulf of Oman into a transit centre for trade between Iran, India and Afghanistan and central Asia generally, bypassing Pakistan.
Earlier this year, India approved a $150 million project to develop Chabahar.
India still owes Iran $6.5 billion that Tehran was unable to recover because of the international sanctions.
Iranian media said a first tranche of this debt, the equivalent of $750 million, was paid into accounts held by the Iranian central bank in Turkey.