Tallies put the Conquest Alliance of pro-Iranian former paramilitary fighters who helped battle Daesh in second place, followed by incumbent Prime Minister Haider al-Abadi's bloc.
The votes in the Kurdish provinces of Dohuk and Kirkuk are still to be counted, but their results will not affect al-Sadr's victory.
A political outlier before Saturday's ballot, Sadr is best known for leading the "fearsome" Mehdi Army in two insurgencies against United States troops in Iraq, following the toppling of Saddam Hussein in 2003.
Sadr has led two uprisings against USA forces in Iraq and is one of the few Shia leaders to distance himself from Iran.
"We are ready to work and cooperate in forming the strongest government for Iraq, free of corruption", Abadi said in a live televised address.
Projecting himself as an Iraqi nationalist, Sadr has a zealous following among the young, poor, and dispossessed among Shia Iraqis, but had been sidelined by influential Iran-backed figures.More news: DeAngelo Hall Retires from NFL After 14-Year Career
Sadr will not become prime minister, as he wasn't on the ballot, but a victory would allow him to appoint someone to the post.
Under article 76 of Iraq's constitution, the right to form a government falls to the political bloc with the most seats. Whoever wins the most seats must negotiate a coalition government in order to have a majority in parliament.
Sadr faces a hard act to herd together enough groups from across Iraq's fragmented political spectrum to form a government. The elections were held Saturday, with low turnout.
Only 44.52 percent of about 24 million people eligible to vote participated in the consultation, a decrease of 15 percentage points, compared to 2014.
Shiite scholar Moqtada al-Sadr, who heads the unit "In motion", won at the parliamentary elections in Iraq, announced with whom he will negotiate.