In a post on X on Friday, the top diplomat said the Islamic Republic welcomed the choice by the Coordination Framework, a coalition of Shia political parties, which is Iraq’s largest parliamentary bloc.
"I congratulate my brother Ali Faleh al‑Zaidi on his appointment," he added.
Araghchi further wished Zaidi success in forming the government and serving the Iraqi people.
"Iran reaffirms its respect for the sovereignty of Iraq and its support for political stability, development, and the strengthening of [bilateral] cooperation in a way that serves the interests of both nations."
The choice of Ali Faleh al-Zaidi, announced by the coalition on Thursday, brought an end to a political stalemate that had persisted for months.
Nouri al-Maliki, head of the State of Law Coalition, had been widely seen as the leading contender for the premiership after elections in November.
The Coordination Framework later announced that both Maliki and the outgoing prime minister, Mohammed Shia al-Sudani, had stepped aside from the race.
In a statement unveiling Zaidi’s nomination, the coalition expressed appreciation for the "historic and responsible" decisions by Maliki and Sudani to withdraw, saying the move helped resolve the political impasse. Sudani also issued a separate message congratulating Zaidi.