After being sidelined by Iranian-backed rivals for years, the apparent parliamentary victory marks a political comeback for Sadr, who didn't even officially run for prime minister in this year's elections.
A political outlier before Saturday's ballot, Sadr is best known for leading the "fearsome" Mehdi Army in two insurgencies against U.S. troops in Iraq, following the toppling of Saddam Hussein in 2003. More than 2 million people are displaced by war, majority Sunnis. In 2014, he reorganized his fighters under the name the Peace Brigades Saraya Salam.
Also in the mix is ex-prime minister Nuri al Maliki, a divisive figure blamed for losing territory to Daesh and stirring sectarianism, who has cultivated ties with Iran.
Under article 76 of Iraq's constitution, the right to form a government falls to the political bloc with the most seats.
It may be Abadi, Reuters reports, who has signaled a willingness to work with Sadr to form a working government.
Al-Abadi directed Iraqi forces to retake the city late previous year after the Kurdish regional administration organized a referendum on independence that controversially included Kirkuk; federal forces moved in with little bloodshed as Kurdish forces withdrew.
According to preliminary results, second in the vote came Iranian-backed militia leader Hadi al-Amiri, while the current PM al-Abadi's coalition was only third.
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If confirmed by Iraq's electoral commission, the results could upend the nation's political balance.
Members of the election commission read out vote tallies for each candidate list in 10 provinces on national TV. After the 2003 United States invasion, Mr Al Sadr formed the Mahdi army militia to fight American troops and later commanded his paramilitary forces against ISIS.
Celebrations erupted in Baghdad's Sadr City, an impoverished quarter that is home to about 3 million people and is named after the cleric's father, Ayatollah Mohammed Sadeq al-Sadr, who was killed by suspected agents of Saddam Hussein in 1999.
The announcement came just over 24 hours after polls closed across the country amid record low voter turnout.
Seats in parliament will be allocated proportionately to coalitions once all votes are counted.
Counting is still ongoing but Sadr's coalition - which is dominated by the Sadrist Movement and the Iraqi Communist Party - is believed to have won at least 54 of the 329-seat parliament, making it the largest political forces in the country, according to Al Jazeera.
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.