The telecoms regulator sold the licenses to five winning bidders for less than the expected forecast of £3.5bn.
The winning bidders are Everything Everywhere, Hutchison 3G UK, BT subsidiary Niche Spectrum Ventures, Telefonica (O2) and Vodafone.
4G mobile broadband is expected to provide superfast download speeds for smartphone and tablet computers. However, the auction raised much less than the £22bn made from the 3G auction in 2000.
Ed Richards, Ofcom chief executive, told BBC News that the amount was lower because "we are in very, very different times".
"What we were trying to do was ensure that a valuable economic resource was brought into productive commercial use," said Richards.
Ofcom have stated that 4G will provide £20bn worth of benefits for UK users over the next 10 years.
The spectrum was auctioned in two bands - 800MHz and 2.6GHz - which are two-thirds of the radio frequencies currently used by tablet computers, smartphones and laptops.
Richards added: "This will allow 4G networks to achieve widespread coverage as well as offering capacity to cope with significant demand in urban centres.
"4G coverage will extend far beyond that of existing 3G services, covering 98% of the UK population indoors - and even more when outdoors - which is good news for parts of the country currently underserved by mobile broadband".
Vodafone bid the highest amount of £791m for five portions of the spectrum.
A Treasury spokesperson said of the announcement: "The £3.5bn number at Autumn Statement 2012 was certified by the independent OBR and based on external expert independent analysis based on similar auctions, including the last 3G one.
"The final auction revenue will be accounted for at Budget in the usual way."
However, Chris Leslie, the shadow chief secretary to the Treasury, said: "It's extremely worrying that the Chancellor's entire budgetary strategy seems to be based on numbers that were significantly over-estimated."
John Redwood MP, added: "The figure for the 4G auction was optimistic, just like most of the numbers in George Osborne's strategy. This is a dent, but there are far bigger dents in the public finances."