With less than a day to go, the Frontier Developments project has raised £1.45m and attracted more than 24,000 backers.
Having smashed the £1.4m barrier, the game will also be released on Mac, approximately three months after its PC release.
Should the project raise £1.5m, the development team will add a further ten ships to the final release.
The Frontier Developments website will continue to accept donations after the Kickstarter appeal closes, with users able to donate using PayPal.
Speaking about the success of the campaign, Frontier's David Braben said: "Thank you to everyone who helped us reached that total - it's incredibly heartening and uplifting to see so many people supporting Elite: Dangerous.
"The help, feedback and ideas given and the enthusiasm shown has been remarkable, vividly illustrating the power of the community which is a force to be reckoned with in today's connected society.
"This has made us even more determined than ever to produce a game worthy of such support and engage even further throughout development."
Elite: Dangerous is being billed as a natural successor to the original Elite and its sequel Frontier, with 3D graphics and multiplayer support.
Players will start out with a small craft and modest resources, but can trade, pirate and bounty hunt their way to wealth and power in a procedurally-generated open world.
Elite: Dangerous is targeted for release on PC in 2014.