Everything Everywhere gets 4G
The move means 4G, which allows much faster downloads, could launch in the UK earlier than previously planned.
Ofcom said the move would deliver "significant benefits" to consumers that outweigh any competition concerns.
But Vodafone and O2 expressed surprise and disappointment at the decision.
Ofcom plans to auction 4G bandwidth to other providers next year.
Everything Everywhere will be allowed to offer 4G services from 11 September.
But, as the regulator pointed out, the timing will be a commercial decision for the company itself. The operator has been trialling 4G services at a number of local businesses in Cumbria in the north of England since the end of June.
Ofcom said delaying the mobile operator from launching 4G would be "to the detriment of consumers".
'Hugely disappointed' Everything Everywhere itself said the regulator's decision was "great news for the UK".
"4G will drive investment,
employment and innovation and we look forward to making it available
later this year, delivering superfast mobile broadband to the UK," the
company said.
They claim that they are disadvantaged as only Everything's spectrum can be reconfigured to handle 4G, while they will have to wait to buy spectrum at an auction next year.
"We are hugely disappointed with today's announcement, which will mean the majority of customers will be excluded from the first wave of digital services," said a spokesperson for O2.
Vodafone was more forthright, saying it was "shocked" at Ofcom's decision.
"The regulator has shown a careless disregard for the best interests of consumers, businesses and the wider economy through its refusal to properly regard the competitive distortion created by allowing one operator to run services before the ground has been laid for a fully competitive 4G market," a company spokesperson said.
Analysts said the two companies were right to be concerned, with the examples of other countries suggesting those network providers that got a head start on their rivals were often able to build successful 4G networks.
"Everything now has a golden opportunity to establish an early lead in the UK's 4G market, but it will only be able to exploit this window if it is able to build a successful launch strategy," said Thomas Wehmeier at Informa Telecoms & Media.
He said much would now depend on the company's ability to persuade mobile phone manufacturers to build smartphones capable of working on its 4G network.
Everything Everywhere has also announced that it will sell some of its 4G spectrum to rival Three.
This was a condition of the European Commission allowing the 2010 merger of Orange and T-Mobile in the UK.
Three's chief executive Dave Dyson said this deal would "more than double the capacity available to customers".
As Everything is not obliged to make the spectrum available until September 2013, this deal will not give Three a head start in launching its own 4G services, however.
Ofcom has issued Everything Everywhere with licences to launch what are called Long-Term Evolution (LTE) services. This is one of a number of broadband technologies that allow the transfer of high-bandwidth data such as video streaming and mapping services.
Other mobile phone networks will be allowed to bid for 4G bandwidth early next year.
The auction will offer the equivalent of three-quarters of the mobile spectrum currently in use - some 80% more than released in the 3G auction which took place in 2000.
Ofcom wants to see at least four wholesalers of 4G mobile services, so that consumers will benefit from better services at lower prices.
The auction will sell chunks of radio spectrum to support 4G, which will allow users to download data such as music and videos at much faster speeds.