Rowhani will become president once supreme leader Ayatollah Ali Khamenei, the ultimate decision-maker in the Islamic republic, formally endorses his surprise June election.
That ceremony, attended by top officials, will take place on August 3, deputy speaker Mohammad Reza Bahonar said in remarks reported by the state broadcaster's website.
A day later, on August 4, Rowhani will take the oath of office before parliament and will then have two weeks to form his proposed cabinet, Bahonar said.
Rowhani won more than 18.5 million votes, or 50.7 percent of total ballots cast i last month's election, overwhelmingly sweeping aside his conservative rivals.
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His win was seen as a rejection of Ahmadinejad's controversial policies.
The 64-year-old mid-ranking Shiite cleric has vowed to form a government that bridges the divide, using skilled experts from the conservatives as well as currently marginalised reformists.
Rowhani says he aims to ease international tensions over Tehran's nuclear ambitions and to resolve domestic woes, including economic hardships exacerbated by Western sanctions targeting the country's vital oil income.