The House of Representatives passed the bill by unanimous consent, meaning without any voiced opposition, after the Senate did the same Monday.
It now goes to President Barack Obama's desk.
While the White House has already signalled that a visa for Iran's appointed UN envoy Hamid Aboutalebi was "not viable," White House spokesman Jay Carney declined to say whether the president would sign the legislation.
Iran has slammed the White House decision as "unacceptable."
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The hostage crisis proved to be a critical turning point in US-Iran relations, leading Washington to sever its diplomatic ties with Tehran.
Aboutalebi, a veteran diplomat who currently heads President Hassan Rouhani's political affairs bureau, has insisted he was not part of the hostage-taking in November 1979, when students seized the US embassy after the overthrow of the pro-Western shah.
He has acknowledged he served a limited role as a translator for the students.
The bill ensures "that we do not have an Iranian terrorist walking the streets of New York city and having diplomatic immunity," Lamborn, a sponsor of the legislation, told his House colleagues.
As the host government, the United States is generally is obliged to issue visas to diplomats who serve at the United Nations.
It is believed that Washington has never denied a visa for a UN ambassador, although Tehran withdrew its nominee once in the early 1990s.
Washington could decide to sit on Aboutalebi's visa application, as it did last year in the case of Sudanese President Omar al-Bashir, an accused war criminal, who sought to address the UN General Assembly.