At a joint press conference with Amiri in the holy city of Najaf on Tuesday, Sadr hailed the formation of "a true alliance to accelerate the formation of a national government away from any dogmatism".
"Our meeting was a very positive one, we met to end the suffering of this nation and of the people. Our new alliance is a nationalist one," Sadr said.
Sadr's Sairoon Alliance won the parliamentary elections with 54 seats but fell short of a majority in the 329-seat parliament.
Amiri's Fatah (Conquest) Coalition came second with 47 seats, while Prime Minister Haider al-Abadi's Nasr (Victory) Coalition once seen as the frontrunner, came in third.
The two figures said they would keep the door open for other winning blocs to join them in forming a new government.
"Fatah and Sairoon announce forming the nucleus of the largest bloc and call on all winning blocs to participate in this alliance under a government programme agreed upon by all that is suitable to face the challenges, crises, and problems facing Iraq," a Fatah spokesman said in a statement.
The alliance, which together has 101 seats, 64 short of the majority needed to form a government, came hours after Prime Minister Abadi urged politicians to keep negotiating over government formation despite an impending nationwide manual recount of votes.