Cesare Prandelli resigned as Azzurri coach after they were knocked out in the World Cup group stage.
Former Italy midfielder Conte, 45, quit as Juventus boss last month, having won the Serie A title in each of his three seasons in charge.
He has also managed Bari and Siena to promotion from Serie B, as well as having spells at Arezzo and Atalanta.
The Italian Football Federation said in addition to his salary, Conte would receive a bonus for qualifying for Euro 2016, an added bonus for climbing at least five places in the Fifa rankings - Italy are currently 14th - and a third bonus if they reach the final of Euro 2016.
Conte is the second big appointment by the Italian Football Federation this week.
Carlo Tavecchio, who made a racist comment during his election campaign, was named as its new president.

14 January 2016 Last updated at 07:55 GMT
A special ship will drill more than 5000 metres down through the ocean floor to reach the super hot rocks of the planet's crust.
The team have picked an area in the Indian Ocean because the earth's crust is thinner there than in other places.
They also hope to find out if anything can survive the heat and pressure to live down there.
Watch Leah's report to find out more...

They arrested 57 people in Barcelona, Valencia, San Sebastian and Las Palmas in the Canary Islands.
Chinese nationals illegally living in Spain reportedly paid the ring €8,000 ($8,960; £6,820) each to obtain fake contracts as domestic workers.
In return they were given residency permits to work in Barcelona.
"They would return to Barcelona once they obtained a residency permit to work in the textile sector, without ever carrying out the job they were hired for," a Spanish police statement said.
The ringleaders, a Chinese couple,  allegedly paid employers between €1,500 and €2,000 for the contracts.
Most of the employers allegedly involved are linked to the hotel trade in Lanzarote, one of the Canary Islands.
Chinese immigrants are the fifth biggest foreign community in Spain with almost 170,000 people as of 2015, according to the National Statistics Institute.

The skull of an adult male was found by the M54 slip road on Thursday by workers surveying a roundabout near Telford.
The find sparked a West Mercia Police inquiry and led to the discovery of "further skeletal remains".
The remains have now been recovered and post-mortem tests on Tuesday will help to identify him, police said.
Officers said the remains had been there for at least two years.
Police have contacted neighbouring forces asking for information about people who had been reported missing.

A spokesman said both men were in their 60s, but gave no further details.
The men reportedly ran into bad weather as they were coming down the mountain over the weekend.
Last week, the remains of two Japanese climbers who disappeared 45 years ago were found on the Matterhorn, one of Europe's highest mountains.
DNA tests helped identify those remains - the latest to have been discovered with the melting of ice on the mountain.
The 4,478m (14,700ft) Matterhorn has a distinctive pyramid-shaped peak, making it one of the world's most recognisable mountains.
Hundreds of people have died trying to reach the top.

Kevin Paddick, 34, of Rosemary Road, Clacton, Essex, is accused of killing Danny Myers, 23, from Enfield.
Mr Myers died in hospital after he was stabbed at an address in Rochford Road, St Osyth, in the early hours of Monday.
The accused is expected to appear before magistrates later. A 29-year-old woman from Clacton, who was arrested on suspicion of murder, has been released without charge.
Italy have appointed former Juventus boss Antonio Conte as their new coach until 2016.
[NEXT_CONCEPT]
Scientists hope to find out more about how our planet was formed by studying the rocks buried deep under our feet.
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Spanish police say they have dismantled a nationwide network that illegally regularised the working status of Chinese immigrants in Spain.
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A post-mortem examination is to take place on human remains found near a motorway slip road in Shropshire.
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Two Japanese climbers who scaled the Matterhorn in the Swiss Alps have been found dead on the mountain, according to the Japanese foreign ministry.
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A man has been charged with murdering a man who was stabbed to death.