The facility will support the sustainable extraction and processing of minerals used in clean energy technologies, such as wind, solar and batteries.
The fund evolved from a recent World Bank report, which found that demand for strategic minerals would skyrocket.
Lithium, graphite and nickel demand is projected to increase by 965%, 383% and 108%, respectively, by 2050.
The fund is targeting total investment of US$50 million over five years.
"The World Bank supports a low-carbon transition where mining is climate-smart and value chains are sustainable and green," World Bank senior director and head of the energy and extractives global practice Riccardo Puliti said.
"Developing countries can play a leading role in this transition: developing strategic minerals in a way that respects communities, ecosystems and the environment.
"Countries with strategic minerals have a real opportunity to benefit from the global shift to clean energy."
Rio Tinto, Anglo American and the German government are backing the fund.
Rio CEO J-S Jacques said the transition to clean energy solutions presented both a significant opportunity and responsibility for the mining industry.
"We want to be part of the solution on climate change and the best solutions will come from innovative partnerships across competitors, governments and institutions," he said.
"Our collaboration with the World Bank and many others is aimed at making a real difference by promoting sustainable practices across our industry.
"We look forward to supporting the Climate-Smart Mining Facility by contributing not just funding but also expertise as a leader in sustainable mining practices."
In February, Rio published its first climate change report, and overnight, also announced it would move from coal-fired power to renewable energy at its Kennecott copper operation in Utah.
Anglo said it shared the World Bank's view that the energy transition would be mineral-intensive, creating economic opportunities for resource-rich countries and the mining sector.
"To have real impact we must work together with governments and operators to bring changes," Anglo CEO Mark Cutifani said.
"Mining cannot continue its long path of simply scaling up to supply what the world needs. We need to do things in dramatically different ways if we are to transform our footprint and be valued by all our stakeholders.
"Our first responsibility is to reduce our energy and water usage, and our emissions. At Anglo American, we have set ourselves on a journey to carbon neutrality operationally, with our 2020 and 2030 targets as staging posts. Our FutureSmart Mining technologies will be a key driver of this."