Economic development minister Carlo Calenda said in a statement that the offer was worth 1.8 billion euros ($2.02 billion).
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ArcelorMittal's partnership with Italy's Marcegaglia had been competing for the takeover with a consortium built around the Indian company Jindal South West Steel, and reports late last week suggested the latter had upped its offer.
But officials said ArcelorMittal — accounting for 85 percent of the bid — and Marcegaglia, which makes up the rest, had prevailed with their bid.
The two have signed a pre-accord with Italian bank Intesa Sanpaolo, which is set to join their consortium Am Investco Italy.
The government said ArcelorMittal had pledged to invest 2.4 billion euros in Ilva, in addition to the purchase price.
Ilva was nationalised and placed under special administration in 2015 after the Riva family, which owned it, was accused of failing to prevent toxic emissions from its Taranto site in southern Italy.
The government quickly opened a tender for the heavily indebted company, which used to produce a third of Italy's steel output.
Officials said the state would now appoint commissioners to negotiate “possible improvements” to the takeover plan during the transition phase.
The Taranto site, which employs 11,000 people, is at the centre of a huge legal case in which experts cited by prosecutors have charged that 11,550 people have died from toxic emissions in seven years.
The takeover has sparked fears of thousands of job losses, with unions saying that Am Investco Italy plans to cut Ilva's overall staff of 14,200 to 9,400 next year and 8,400 by 2023.
Hundreds of employees at Ilva's site in the northwestern city of Genoa staged a protest on Monday, demanding a meeting with Prime Minister Paolo Gentiloni.