US President Donald Trump reinstated the sanctions against Iran a year ago after abandoning the landmark 2015 nuclear deal between Iran and six world powers.
The field, in the south-western province of Khuzestan and about 2,400 sq km (926 sq miles) in area, contains 53 billion barrels of crude, he said.
"Workers and the exploration arm of the National Iranian Oil Co. have found an oilfield with 53 billion barrels of reserves", Rouhani said in a televised speech in the central city of Yazd.
Oil reserves refer to crude that's economically feasible to extract.
It added that Iran had an estimated 157 billion barrels of proved crude oil reserves in January 2018. Figures can vary wildly by country due to differing standards, though it remains a yardstick of comparison among oil-producing nations.
For scale, Venezuela's oil reserves are the largest in the world at 297 billion barrels while Russia's reserves stand at 80 billion barrels. It shares a massive offshore field in the Persian Gulf with Qatar.
The 80-metre deep field stretches almost 200 kilometres from Khuzestan's border with Iraq to the city of Omidiyeh, Rouhani added.
They were imposed after the USA pulled out of a nuclear deal with world powers previous year.
Iran has been struggling to sell oil overseas because of tough United States sanctions. It just began injecting uranium gas into centrifuges at an underground facility as well. Tehran denied the allegation, though it did seize oil tankers and shoot down a USA military surveillance drone.