Virgin boss Sir Richard Branson launched the competition today in London alongside former US vice-president Al Gore.
A panel of judges will oversee the prize, including James Lovelock and Nasa scientist James Hansen.
Sir Richard said humankind must realise the scale of the crisis it faced.
"The Earth cannot wait 60 years," he said at the news conference. "I want a future for my children and my children's children. The clock is ticking."
He said if the planet was to survive, it was vital to find a way of getting rid of the greenhouse gas carbon dioxide.
He said he believed offering the $25m (£12.5m) Earth Challenge Prize was the best way of finding a solution.
Moral challenge
Overseeing the innovations are James Hansen, the noted climate scientist and head of the Nasa Institute for Space Studies; the inventor of Gaia theory James Lovelock; UK environmentalist Sir Crispin Tickell; and Australian mammalogist and palaeontologist Tim Flannery.
They are looking for a method that will remove at least one billion tonnes of carbon per year from the atmosphere.
Al Gore, the former presidential candidate turned environmental campaigner, is also on the judging panel.
He said: "It's a challenge to the moral imagination of humankind to actually accept the reality of the situation we are now facing.
"We're not used to thinking of a planetary emergency, and there's nothing in our prior history as a species that equips us to imagine that we, as human beings, could actually be in the process of destroying the habitability of the planet for ourselves."
His recent film, An Inconvenient Truth, focused on global warming.
Stuart Haszeldine, professor of geology at the University of Edinburgh, commented: "Richard Branson is ahead of the pack in getting to grips with CO2 in the atmosphere.
"His decisive action places shame on the dithering of the UK Treasury, who will not let British power companies build CO2 capture plants, in case they are too expensive.
"I hope all other businesses, large and small, follow his lead. Yes, it's true Branson's company may benefit eventually, but we will all benefit, by a cleaner, greener planet. We all share the same atmosphere."
Carbon capture and storage is already a key area of research.
Scientists have been looking into removing the greenhouse gas from the atmosphere and storing it in oil and gas fields, injecting it deep into the ocean, or chemically transforming it into solids or liquids that are thermodynamically stable.
However, these methods have raised concerns, notably because of the possibility of leakage from the storage sites and fears that C02 dissolved in large quantities in the ocean might harm marine ecosystems.
Other scientists are also looking at schemes that might "scrub" the air of CO2, collecting the gas for safe storage; but many critics say the energy required to achieve this would make such an approach self-defeating.
Sir Richard Branson has already pledged to invest $3bn (£1.6bn) in profits from his travel firms, such as airline Virgin Atlantic and Virgin Trains, towards research into renewable energy technologies.
