Ofcom warned in February it would shorten O2's 3G licence if it did not comply with the roll-out obligation by June 30.
The regulator says the target has now been achieved.
The other four holders of 3G licences, including Vodafone and T-Mobile, complied with Ofcom's original requirement for the end of December - at which stage O2's network covered 75.69 per cent of the population, a shortfall equivalent to around 2.5m people.
O2 acquired its 3G licence in 2000 for £4bn. It is due to run until December 2021, but Ofcom could have reduced this to August 2021 - at an estimated cost to O2 of at least £40m.
The company, owned by Spain's Telefonica, had targeted areas of most demand.
The 3G technology enables consumers to watch video and television and access the internet via mobile phones.
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