Culture Secretary Matt Hancock also announced a rival bid from USA media giant Comcast had been given the green light, in a move that is likely to set up a multibillion-pound bidding war for the British broadcaster.
The U.K. approval allows Fox to increase its 10.75 pounds-a-share bid for the 61 percent of Sky it doesn't already own to fend off a rival offer from Comcast, which is 16 percent higher.
United Kingdom culture minister Matt Hancock said the deal can move forward if Sky News is sold to a suitable third party. There had been concerns that the 21st Century Fox-Sky deal would give the Murdoch family too much influence over public opinion.
Sky also notes the Secretary of State's final decision not to intervene on public interest grounds in relation to the Comcast offer for Sky.
The U.K. plans to approve 21st Century Fox Inc.'s proposed 11.7 billion-pound ($15.6 billion) takeover of Sky Plc, a crucial victory for Rupert Murdoch as he battles Comcast Corp. for control of the country's largest pay-TV company.
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Sky News would have to be sold off to maintain a diverse broadcasting landscape.
Fox's offer values Sky at around £18.5 billion.
Fox said that it has already submitted proposals to divest Sky News to Disney.
But he said he needed to be sure that Sky News remained financially viable over the long term, was able to operate as a major UK-based news provider and was able to take its editorial decisions independently.
"As a result, I have asked my officials to begin immediate discussions with the parties to finalise the details with a view to agreeing an acceptable form of the remedy, so we can all be confident Sky News can be divested in a way that works for the long term".
"That might be good for shareholders but it's the minister's duty to protect the interest of the public".