
Branson, whose Virgin Media re-brand of NTL/Telewest was unveiled this week, claimed that his Earth Challenge offers the biggest prize in history.
Speaking at the London launch, Branson invited entrants to devise a system that removes one billion tonnes or more of carbon dioxide from the atmosphere every year for at least a decade.
Branson's five co-judges include former US vice president Al Gore, Nasa Goddard Institute director Jim Hansen and Gaia theorist James Lovelock.
Steve Howard, chief executive of the Climate Group, and an advisor to the judges, said: "For US$25m, people will do extraordinary things. This is to fire people up and say: 'Let's do this.'"
Branson explained that the prize was inspired by the 18th century £20,000 ($50,000) award for measuring longitude, won by clockmaker John Harrison.
Branson also cited the US$10m X-Prize for private human spaceflight, won in 2004 by the Tier One project using the experimental SpaceShipOne.
Scientists have three years to crack the greenhouse problem, and the closing date for submissions is 8 February 2010. It will re-open for two years if the judges do not deem any submissions worthy of the prize.
Carbon capture and sequestration technologies are not eligible to win, as this established technology involves the removal of emissions from power plants before they reach the atmosphere.
Friends of the Earth gave the initiative a cautious welcome, saying that it should not distract from the need to reduce emissions "including unsustainable air travel".
Edinburgh University geologist Stuart Haszeldine was less equivocal. He told New Scientist magazine: "Richard Branson is ahead of the pack in getting to grips with CO2 in the atmosphere. I hope all other businesses, large and small, follow his lead."