The agency, Aria, will be run along the lines of US equivalents that were instrumental in the creation of the internet and GPS.
Aria, which has £800m funding over four years, will have a "higher tolerance for failure than is normal", the government said.
Labour said the government needed to clarify what the agency would do.
The new body - the Advanced Research & Invention Agency (Aria) - would fund "high-risk, high-reward" scientific research, the government said.
But the amount of funding it will get is a fraction of the money pumped into existing government research bodies such as UK Research and Innovation (UKRI).
For 2020-21 alone, the government has allocated £10.36bn for its research programmes and bodies.
Nevertheless, the government said that Aria would "help to cement the UK's position as a global science superpower".
Business Secretary Kwasi Kwarteng said the new agency would "drive forward the technologies of tomorrow" by "stripping back unnecessary red tape".
"From the steam engine to the latest artificial intelligence technologies, the UK is steeped in scientific discovery. Today's set of challenges - whether disease outbreaks or climate change - need bold, ambitious and innovative solutions.
"Led independently by our most exceptional scientists, this new agency will focus on identifying and funding the most cutting-edge research and technology at speed," Mr Kwarteng said.
Boris Johnson's former senior adviser Dominic Cummings was a prominent supporter of "blue-sky" thinking by small groups of scientists, saying in 2019 funding should be given to "high-risk high-payoff visions".
It was the sale of the UK's artificial intelligence startup DeepMind to Google in 2014 which apparently got Dominic Cummings thinking.
The man who was to become Boris Johnson's chief advisor became obsessed with the idea that the UK was giving away its technological crown jewels.
The answer, he decided, was to create a British version of Arpa, the American agency credited with funding the development of the internet and GPS.
Despite Mr Cummings' departure from Downing Street, the government has opted to go ahead with Aria, an agency designed to make big bets on risky projects.
It will have a tiny fraction of the budget of the existing research agency UKRI, which will carry on doing its job.
But Aria will apparently be independent, freed from bureaucracy and imbued with a Silicon Valley culture where failure is not to be feared.
The test, of course, will be whether there are also successes to celebrate.
Aria will be modelled on the influential US Advanced Research Projects Agency (Arpa), which supported research that led to the internet and GPS, and its successor Darpa, which funded the precursors to today's coronavirus vaccines.
Science and innovation minister Amanda Solloway said: "To rise to the challenges of the 21st Century, we need to equip our R&D community with a new scientific engine - one that embraces the idea that truly great successes come from taking great leaps into the unknown."
Recruitment for a chief executive and chair for the agency will begin in the coming weeks.
Matthew Fell, CBI UK chief policy director, said the UK had "a unique opportunity to play to its strength" with the new agency, to help create jobs, raise productivity and tackle the biggest challenges facing the country.
"Key to Aria's success will be strong business engagement to make sure the brilliant ideas developed can make it through to market," he added.
Sir Jim McDonald, president of the Royal Academy of Engineering, said: "Engineering is central to an ambitious innovation agency of this kind, forming the bridge between research and innovation to enable technological and commercial breakthroughs."
But Labour shadow business secretary Ed Miliband said the agency needed to have a clear mandate and to be subject to Freedom of Information laws, to ensure transparency of funding.
"Labour has long called for investment in high ambition, high risk science," he said. "But government must urgently clarify the mission and mandate of this new organisation, following strong engagement with the UK's science base - those closest to the work."
Change before you have to.