The cash comes from "efficiency savings" and money returned by BT as part of the government's flagship broadband rollout scheme.
Superfast speeds - measured at 24Mbps - allow families to watch TV on multiple devices at the same time, or let children do homework while parents do online banking and shopping.
Steve Unger, Ofcom's group director, said it was unacceptable that so many people were struggling to get broadband.
Culture Secretary Karen Bradley said the funds would help to bring faster speeds to homes and businesses in some of the most remote parts of the UK by 2020.
Experts said it was not all "new money" but would still be welcomed.
The cash will be made up of £150m in cost savings and the rest in the form of returned subsidies from BT, the government said.
Under a 2010 deal, the government paid BT to roll out superfast broadband in hard-to-reach areas where providers had said it was not cost-effective to install broadband infrastructure.
As part of the agreement, if more than 20% of premises in those areas bought superfast broadband, BT had to repay some of the subsidy.
On average, the take-up has been 30.6%, leading to a forecast repayment of £292m, the Department for Culture, Media and Sport said.
To the government and BT it's that rare thing, a public/private partnership which is actually going to come in under budget and deliver more than was promised.
The extra funds will be spent in all areas of the country through the Broadband Delivery UK scheme.
Ministers said the technology is ideal for most businesses too, allowing bosses to run websites and buy and sell online.
The government has not set a timeline for when the 600,000 premises will benefit.
It comes after Chancellor Philip Hammond announced £1.14bn in government funds in last month's Autumn Statement to improve fibre broadband and develop 5G.
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