A declaration announced as part of a United Nations summit on climate change being held in New York also pledges to halve the rate of deforestation and to restore hundreds of millions of acres of degraded land over the next 16 years.
Backers of the New York Declaration on Forests claim their efforts could save between 4.5 billion and 8.8 billion tonnes of carbon emissions annually by the end of the next decade.
The savings add up to the equivalent of taking all the world’s cars off the road.
The UK, Germany and Norway have pledged to enter into initiatives worth up to £700 million over the next couple of years to pay countries for reducing deforestation.
Firms including Kellogg’s, Marks & Spencer, Barclays and Nestle, as well as charities such as the RSPB and WWF, have signed the statement.
Supporters say saving natural forests is a crucial step in limiting global temperature rises to 2C, the internationally agreed maximum for avoiding catastrophic climate change.
The declaration comes after studies suggest changes in land use such as felling trees for agriculture or development accounts for around 8 per cent of global emissions of climate-warming carbon dioxide.
“Forests represent one of the largest, most cost-effective climate solutions available today,” it states.
“Action to conserve, sustainably manage and restore forests can contribute to economic growth, poverty alleviation, rule of law, food security, climate resilience and biodiversity conservation.”
Signatories are committing to a number of steps, including backing a private-sector goal of eliminating deforestation from producing agricultural products such as palm oil, soy, paper and beef by no later than 2020.
They are also seeking to support alternatives to deforestation caused by subsistence farming and using wood as fuel, with rewards for countries that reduce emissions from tree-felling.
The declaration is a key announcement at the summit, convened by UN secretary-general Ban Ki-Moon.
Mr Ban said: “Forests are not only a critical part of the climate solution – the actions agreed today will reduce poverty, enhance food security, improve the rule of law, secure the rights of indigenous peoples and benefit communities around the world.”
David Cameron and US president Barack Obama joined more than 120 world leaders at the event, which aims to drive action ahead of talks in Paris next year to agree a new climate treaty.
The Prime Minister said he will push for a target of reducing greenhouse gas emissions in Europe by at least 40 per cent.
But Friends of the Earth said: “David Cameron’s warm words on climate change are completely undermined by his policies at home – massive tax breaks for oil exploration and support for fracking will simply keep our economy hooked on dirty fossil fuels.”