"I am now very sad to have to report that she has died as a result of her injuries," West Yorkshire Police chief Dee Collins told reporters.
Cox was pronounced dead at 1:48pm (1248 GMT), Collins told a press conference in Wakefield, northern England.
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The attack happened in the village of Birstall, near Wakefield, in Cox's constituency.
Police have arrested a 52-year-old man.
"We are trying to establish what we do know about this gentleman," said Collins.
"At the moment the enquiries have just started.
"We are not in a position to discuss any motive at this time," she said, but added: "We are not looking for anyone else in connection with this incident."
Cameron says death of lawmaker Jo Cox is a tragedy
The death of Cox is a tragedy, British Prime Minister David Cameron said.
"The death of Jo Cox is a tragedy. She was a committed and caring MP (Member of Parliament). My thoughts are with her husband Brendan and her two young children," he said on Twitter.
The death of Jo Cox is a tragedy. She was a committed and caring MP. My thoughts are with her husband Brendan and her two young children.
— David Cameron (@David_Cameron) June 16, 2016
After the attack, the "Remain" camp said it was "suspending all campaigning for the day" while a spokesperson for the rival Vote Leave group said their 'battle bus' was returning to headquarters.
Cameron cancelled a planned rally during a historic but controversial visit to Gibraltar as part of his campaign for Britain to stay in the EU in the June 23 vote.
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