The announcement came at a press conference four hours after the mum-of-two, 41, was attacked outside a library
The announcement came at a press conference four hours after the mum-of-two, 41, was brutally attacked outside a library in Birstall, West Yorkshire.
Ms Cox was due to hold a constituency surgery when she was shot, reportedly three times, and left in a critical condition just before 1pm.
West Yorkshire Police said she was pronounced dead at 1.48pm by a paramedic team.
Temporary Chief Constable Dee Collins said: "This is a very significant investigation with large numbers of witnesses being spoken to police at this time."
Read more: MP Jo Cox shot and injured: Live updates
"A full investigation is under way to establish the motive of this attack."
West Yorkshire Police and Crime Commissioner Mark Burns-Williamson said: "All our thoughts and prayers are with Jo's family at this time.
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"This is a truly shocking incident but I want to try and reassure communities that our information is that this is a localised incident, albeit one that has a much wider impact."
Labour leader Jeremy Corbyn said in a statement: “The whole of the Labour Party and Labour family - and indeed the whole country - will be in shock at the horrific murder of Jo Cox today.
“Jo had a lifelong record of public service and a deep commitment to humanity. She worked both for Oxfam and the anti-slavery charity, the Freedom Fund, before she was elected last year as MP for Batley and Spen – where she was born and grew up.
“Jo died doing her public duty at the heart of our democracy, listening to and representing the people she was elected to serve. It is a profoundly important cause for us all.
“Jo was universally liked at Westminster, not just by her Labour colleagues, but across Parliament.
“In the coming days, there will be questions to answer about how and why she died. But for now all our thoughts are with Jo’s husband Brendan and their two young children. They will grow up without their mum, but can be immensely proud of what she did, what she achieved and what she stood for.
“We send them our deepest condolences. We have lost a much loved colleague, a real talent and a dedicated campaigner for social justice and peace. But they have lost a wife and a mother, and our hearts go out to them.”
Read more: First picture of man suspected of 'shooting and stabbing' Labour MP Jo Cox outside library
Fears appeared to be confirmed when Ms Cox's husband Brendan tweeted a photo of her on a houseboat they own on the Thames with no caption.
Only yesterday he and her two children joined a joyous flotilla on the river as Brexit campaigners sprayed each other with hoses.
The attack scene remained cordoned off tonight as forensics officers searched under cars for evidence.
Tributes poured in from MPs across the political spectrum including Prime Minister David Cameron and Labour leader Jeremy Corbyn .
Both sides of the EU referendum battle suspended campaigning out of respect.
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Before Ms Cox's death was announced, Rotherham Labour MP Sarah Champion said: "I can't stop shaking. I feel so emotional about this. Jo is the most fantastic woman.