Fox could face further competition from the United States cable giant Comcast, however, after it forced Sky's independent directors to drop their previous backing for Fox with an unexpected £12.50-a-share bid for the group in February.
A top Sky shareholder told Reuters that Comcast is expected to respond with a higher offer for the company.
The fight for ownership of Sky is playing out against the backdrop of Disney and Comcast's battle for a raft of Fox assets, including Fox's current 39% stake in Sky.
Chaplin fears that Comcast could overpay for Sky and possibly Fox, leading to tough ramifications for the company's stock price.
Its offer represents an 82 percent premium to Sky's shares in 2016 before the takeover drama started, and a multiple of 21 times 2017 earnings per share. Comcast has also offered guaranteed funding for Sky News and other commitments, including maintaining Sky's West London base.
The decision by Jeremy Wright clears the final regulatory hurdle for Fox's bid for the 61 percent of Sky that it does not already own.
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Fox shareholders are scheduled to vote on the Disney deal on July 27.
Fox's bid for Sky is the most recent episode in Murdoch's long-running effort to take full control of the company.
The improved bid means Sky investors now have 60 days to weigh up the offers.
USA media giant Comcast threw its hat into the ring in February with a £22bn offer for Sky, trumping an offer from Fox, and starting a bidding war.
KitGuru Says: No matter who ends up getting their hands on Fox's assets, the loss of competition from such a large player in the market is sure to be felt across the entertainment industry.
"Fox coming back in for Sky isn't a surprise in itself, but the fact the offer is slightly behind what some had anticipated brings another twist", said George Salmon, equity analyst at Hargreaves Lansdown. News Corp., which is controlled by the Murdochs, withdrew its bid for Sky soon after. The opposition has not completely subsided despite the plan to spin off Sky News.