He also said he would make an initial €5m ($5.7m) available from central funds to the north-western region.
The regional government had requested the action following Tuesday's disaster, which left 39 people dead.
There has been anger and disbelief in Italy that such a vital structure could have simply given way.
Rescuers have said there is little hope of finding more survivors underneath the Morandi bridge, where dozens of vehicles fell from a height of 45m (148ft) in Tuesday morning's collapse
The cause is not yet known but there has been heavy criticism of the private company responsible for operating the bridge.
What is the latest at the scene?
Hundreds of firefighters worked overnight and throughout Wednesday with lifting gear, climbing equipment and sniffer dogs to try to locate survivors and bodies.
More than 400 people have been evacuated from the area. Residents of housing blocks under one pillar were ready to move back, but were then told it was cracking and that their homes were at risk.
There are 15 people being treated in hospital, nine of them in a serious condition, according to the local prefecture.
What did the PM say?
Giovanni Toti, governor of Liguria, had asked the government in Rome to declare a state of emergency in the region.
Following a cabinet meeting held in the city of Genoa, Prime Minister Conte said: "We agreed to his request to declare a state of emergency in Ligura for 12 months due to the events of yesterday morning... and we decided to release €5m from the national emergency fund for immediate needs."
He announced a national day of mourning would take place, which the government wanted "to coincide with the funerals of the victims".
He added: "These are unacceptable tragedies that should not happen in a modern society. This government will do everything to prevent such tragedies from happening again.
Mr Conte confirmed the government's intention to revoke the contract from private sector firm Autostrade per l'Italia, which was in charge of operating and maintaining the bridge and the A10 motorway it was part of.
The highways firm defended its maintenance record, saying it had checked the bridge every three months using highly specialised techniques.
Who were the victims?
They included families in their cars, people going to work, and people going on holiday.
Most of them were Italians, but the French foreign ministry said four of its nationals had also died.
Among the dead were a family of three - Roberto Robbiano, 44, Ersilia Piccinino, 41, and their young son Samuel.
What have survivors been saying?
One of the most compelling testimonies came from Davide Capello, 33, a former goalkeeper for Serie A side Cagliari.
His car fell 30m in the collapse, but came to rest in a pocket between the columns and he survived.
"I was able to get out... I don't know how my car wasn't crushed. It seemed like a scene from a film, it was the apocalypse," he said.
Valentina Galbusera, 43, a doctor, told La Stampa: "The bridge fell in front of me, not even 20m away, I avoided the collapse by only a couple of seconds. I felt the bridge was shaking and I tried to reverse. Then I got out of the car and started running."
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