Fox’s offer of £10.75 per share for the 61 per cent of Sky it does not already own represents a 40 per cent premium.
The deal, which shareholders will still have to vote on, comes five years after the media tycoon’s last tilt at taking full control of the business through News Corporation.
That bid was derailed after the company – which owns The Sun and The Times – was forced to abandon the bid when it became embroiled in the phone-hacking scandal involving News International.
21st Century Fox said: “The strategic rationale for this combination is clear. It creates a global leader in content creation and distribution, enhances our sports and entertainment scale, and gives us unique and leading direct-to-consumer capabilities and technologies.
“It adds the strength of the Sky brand to our portfolio, including the Fox, National Geographic and Star brands.”
Attention will now turn to culture secretary Karen Bradley, who has until Christmas to decide whether to refer the deal to Ofcom.
A number of Sky shareholders, including Standard Life Investments and Jupiter Asset Management, have questioned the offer price since news of the bid broke last week.
But Martin Gilbert, deputy chairman of Sky and chief executive of Aberdeen Asset Management, has moved to assuage their concerns.
“We, supported by our advisers, believe 21st Century Fox’s offer… will accelerate and de-risk the delivery of future value for all Sky shareholders.
“As a result, the Independent Committee unanimously agreed that we have a proposal that we can put to Sky shareholders and recommend.”
The deal values Sky at some £18.5 billion.