Almost 7,000 candidates from dozens of political alliances are competing for 329 parliamentary seats.
Prime Minister Haider al Abadi facing stiff competition from parties with closer ties to Iran, which holds considerable military and economic sway in the country.
Despite overseeing the defeat of the terrorist group, whose fighters overran nearly a third of Iraqi territory just weeks after he took office in the summer of 2014, Mr Abadi has failed to emerge as the clear favourite due to entrenched corruption and an economic downturn.
The downturn was partly sparked by a fall in global oil prices and the fact that the war against IS cost the Government an estimated $100bn (£73.8bn).
His strongest opponents are his predecessor, Nouri al Maliki, who was in office for eight years, and an alliance of candidates linked to the country’s powerful paramilitary forces.
The alliance – known as Fatah, which is Arabic for Conquest – is led by former transport minister Hadi al Amiri, who later became a senior commander of mostly Shia fighters in the battle against IS.
Another strong candidate is influential cleric Muqtada al Sadr, who commanded a powerful Shia militia that battled US troops in the years after the 2003 invasion. He then mobilised the militia after IS militants swept across northern and central Iraq in the summer of 2014.
Iraq declared victory over IS in December.
Saturday’s election – the fourth since Saddam Hussein was overthrown in 2003 – is being conducted electronically for the first time in a bid to reduce fraud.
Polling centres have also been set up for many of the country’s two million nationals who have been displaced by the war against IS. Iraq has a total population of just around 37 million, with 24 million eligible to vote.
More from Iraq
US military to review security amid Strava fitness app fears
Twin suicide bombings at Baghdad street market kill at least 38
Four Iraqis win damages for unlawful detention and ill-treatment by British forces
‘Mission accomplished’: Hezbollah ready to withdraw from Iraq
Meet Daeshgram: The Iraqi hackers using Islamic State’s propaganda against them
Young IS sniper victim Maryam just wants a normal life
The results are expected by the end of Monday, but coalition negotiations are expected to drag on for months as no single party is likely to win enough seats to hold a majority.
When the new government is formed, it will have to deal from the fallout of US President Donald Trump’s decision to pull out of the Iran deal, which has raised fears among Iraqis that their country could be a battleground for conflict between Washington and Tehran.