Pezeshkian promised no radical changes to Iran's Shi'ite theocracy in his campaign and long has held Supreme Leader Ayatollah Ali Khamenei as the final arbiter of all matters of state in the country.
However he had promised to reach out to the West and ease enforcement on the country's mandatory headscarf law after years of sanctions and protests squeezing the Islamic Republic.
A vote count offered by authorities put Pezeshkian as the winner with 16.3 million votes to Jalili's 13.5 million in Friday's election.
Supporters of Pezeshkian, a heart surgeon and longtime lawmaker, entered the streets of Tehran and other cities before dawn to celebrate as his lead grew over Jalili, a former nuclear negotiator.
But Pezeshkian's win still sees Iran at a delicate moment, with tensions high in the Mideast over the Israel-Hamas war in the Gaza Strip, Iran's advancing nuclear program, and a looming US election that could put any chance of a detente between Tehran and Washington at risk.
The first round of voting on June 28 saw the lowest turnout in the history of the Islamic Republic since the 1979 Islamic Revolution.
Government officials up to Supreme Leader Ayatollah Ali Khamenei predicted a higher participation rate as voting in the run-off got under way, with state television airing images of modest lines at some polling centres across the country.
The late president Ebrahim Raisi, who died in a May helicopter crash, was seen as a protege of Khamenei and a potential successor as supreme leader.
Still, many knew him for his involvement in the mass executions that Iran conducted in 1988, and for his role in the bloody crackdowns on dissent that followed protests over the 2022 death of Mahsa Amini, a young woman detained by police over allegedly improperly wearing the mandatory headscarf, or hijab.
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