The world's richest man said the money would finance work by scientists, activists and other groups.
He said: "I want to work alongside others both to amplify known ways and to explore new ways of fighting the devastating impact of climate change."
Writing on his Instagram account, Mr Bezos said the fund would begin distributing money this summer.
Mr Bezos has an estimated net worth of more than $130bn, so the pledge represents almost 8% of his fortune.
Some Amazon employees have urged him to do more to fight climate change. There have been walkouts and some staff have spoken publicly. Also, Mr Bezos is financing the Blue Origin space programme, criticised for its carbon footprint.
Compared to some multi-billionaires, Mr Bezos had done only limited philanthropy. His biggest donation before Monday's pledge is thought to have been $2bn in September 2018 to help homeless families and fund schools.
He has also been criticised for not signing the Giving Pledge, under which the super-rich promise to give away half of their wealth during their lifetimes.
The Seattle-based company is a neighbour of Microsoft, which in January unveiled a plan to become carbon negative by 2030.
Mr Bezos's full Instagram post read: "Today, I'm thrilled to announce I am launching the Bezos Earth Fund.
"Climate change is the biggest threat to our planet. I want to work alongside others both to amplify known ways and to explore new ways of fighting the devastating impact of climate change on this planet we all share. This global initiative will fund scientists, activists, NGOs - any effort that offers a real possibility to help preserve and protect the natural world.
"We can save Earth. It's going to take collective action from big companies, small companies, nation states, global organisations, and individuals.
"I'm committing $10bn to start and will begin issuing grants this summer. Earth is the one thing we all have in common - let's protect it, together."
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