In his message to Modi, Rouhani expressed hope that Tehran and New Delhi would enhance their relations.
"Undoubtedly, your election, which was marked by mass participation of people from all walks of life, indicates the full confidence of the Indian nation in your developmental and prudent policies," he was quoted as saying by semi-official FARS news agency today.
Rouhani also wished more success for Modi and prosperity for the Indian people.
"The Islamic republic of Iran congratulates the holding of this vibrant election to the (Indian) people, government, political parties and leaders, specially the BJP," Iranian Foreign Ministry Spokeswoman Marziyeh Afkham said.
BJP leader Modi claimed victory on May 16 and was sworn-in yesterday as the 15th Prime Minister of India.