The vote came two weeks after US President Donald Trump's decision to decertify the Iranian nuclear deal, as part of Washington's efforts to toughen its policy toward Iran without undermining the agreement.
Thousands gathered on the campus of the former embassy, called a "den of espionage", where a ballistic missile was displayed.
The United States has also imposed new sanctions over the Islamic Republic's ballistic missile programme.
During a rally on Saturday, Ali Shamkhani, secretary of Iran's Supreme National Security Council, criticized U.S. President Donald Trump, who has refused to re-certify the 2015 Iran nuclear deal.
Mr Trump refused to recertify the 2015 landmark nuclear deal between Iran and world powers in October and the United States has imposed more sanctions on Iran over its ballistic missile programme.
A few months after the toppling of the US -backed government of the Shah Mohammad Reza Pahlavi, Iranian students, believing the USA embassy was being used as cover for espionage activity aimed at overthrowing the Islamic Republic, stormed the building.
"To give in to the Americans makes them more aggressive and insolent".
A crowd chanted "Death to Israel" and "Down with the U.S." during the celebration. State television said similar celebrations were being held in other Iranian cities and towns. Under that deal, most global sanctions on Iran were lifted in exchange for Tehran curbing nuclear activity.
Ali Shamkhani, secretary of the country's Supreme National Security Council, addressed the crowd on Saturday, saying Iran will make any sanctions imposed by the United States "ineffective", even as Washington targets Iran's economic, nuclear and defensive power.
Anti-Iran measures adopted by the U.S. have strengthened the Iranian nation's power, Shamkhani said on Saturday. The U.S. cut its diplomatic relations with Iran after the embassy takeover and has had no diplomatic relations since.
Though U.S. diplomats and Central Intelligence Agency officers shredded thousands of documents before the students entered the building, the Iranian researchers spent years piecing each paper slice back together.