It could also ease tensions that some Iraqi officials fear could lead to an intra-Shi'ite civil war. Amiri, widely described as Tehran's man in Iraq, is one of the most powerful figures in the country, a key US ally and major oil producer.
The election has been a test for both Sadr and Iran.
Tehran is under pressure to maintain its deep influence in Iraq - its most important Arab ally - after the United States pulled out of the nuclear deal, and its Houthi allies in Yemen face the biggest offensive yet from a Saudi-led coalition.
Middle East powers Tehran and Saudi Arabia are waging a proxy war mainly in Iraq, Yemen and Syria.
Sadr, who once led violent campaigns against the US occupation that ended in 2011, has emerged as a nationalist opponent of powerful Shi’ite parties allied with neighbouring Iran and as a champion of the poor.
He has to tread carefully.
Tehran, known for its pragmatism, has skillfully manipulated the formation of Iraq governments in the past and its militia allies are the most powerful forces in the country.
The Sadr-Amiri alliance may serve the purposes of the most powerful sides in Iraq politics as the country tries to rebuild from the devastating war against Islamic State.