Rouhani, a cleric and former nuclear negotiator, bested his conservative counterparts during Iran's presidential elections in June. He is considered a moderate when compared to his rivals.
The Shiite cleric said in response to congratulatory messages from Middle East leaders he would reach out to the international community when he takes office in August.
"Expanding ties with the neighboring countries and strengthening regional cooperation in order to maintain peace and provide the interests of the regional nations is one of the foreign policy priorities of Iran's 11th administration," he was quoted as saying Tuesday by state-funded broadcaster Press TV.
Iran has been criticized for remaining loyal to Syrian President Bashar Assad during the civil war. Iran's nuclear program remains a sore spot for Western countries who suspect Iran's nuclear research is geared toward a weapons program.
Iran denies the allegations, saying it has the right to a peaceful nuclear program as a signatory to the Nuclear Non-Proliferation Treaty.
Iranian Supreme Leader Ali Khamanei has the ultimate say over Iranian policies.