This unprecedented warning comes exactly 40 years since scientists from 50 nations met at the First World Climate Conference in 1979.
They say they "have a moral obligation to clearly warn humanity of any catastrophic threat".
Researchers set out indicators showing the impact of humans on the climate and have urged that "to secure a sustainable future, we must change how we live".
The paper describes "profoundly troubling" signs from activities including sustained increases in human populations, the amount of meat consumed per person, the number of air passengers carried and global tree cover loss, as well as carbon emissions and fossil fuel consumption.
Scientists from the University of Sydney, Oregon State University and the University of Cape Town in South Africa are joined in the warning by 11,000 signatories from 153 countries, including the UK.
The declaration is based on analysis of more than 40 years of publicly available data covering a range of measures from energy use to deforestation and carbon emissions.
The scientists warn that despite 40 years of global climate negotiations, people have largely failed to address the problem of global warming.
Now "the climate crisis has arrived and is accelerating faster than most scientists expected", they say.
But there is hope, the researchers say, setting out six areas where governments, businesses and the rest of humanity can take action to lessen the worst effects of climate change.
Six areas where governments, businesses and the rest of humanity can take action, according to researchers
Replacing fossil fuels with low-carbon renewables and other cleaner sources of energy, alongside implementing massive energy-saving practices.
Reducing harmful pollutants
Prompt action to reduce short-lived climate pollutants such as methane, soot and hydrofluorocarbons (HFCs).
Protecting natural systems
Protect and restore natural systems, such as forests, grasslands, wetlands, peatlands, mangroves and seagrasses which store carbon.
Change in diet
Eating mostly plant-based foods, and reducing animal products will improve human health, cut emissions such as methane and free up land to restore habitats, while there is also a need to protect soil carbon through agricultural practices, and to cut food waste.
Over-exploitation of resources driven by economic growth needs to be curtailed, with a shift from targeting GDP to sustaining ecosystems and improving wellbeing by prioritising basic needs and reducing inequality.
'Gradually reduce' the world population
There is a need to stabilise, and "ideally gradually reduce", the world population, through policies such as making family-planning services available to all people and making primary and secondary education a global norm for all especially girls and young women.
Dr Thomas Newsome, at the University of Sydney, said: "Scientists have a moral obligation to warn humanity of any great threat.
"From the data we have, it is clear we are facing a climate emergency."
Dr Newsome said that measuring global surface temperatures as a marker of climate change will remain important.
He added: "While things are bad, all is not hopeless. We can take steps to address the climate emergency."