The cash offer values Sky shares at 1075p each – less the value of any dividends paid subsequently by Sky – putting a valuation on the company of £18.48bn.

21st Century Fox, whose other media assets include 20th Century Fox, one of Hollywood’s largest studios, currently owns 39.1% of Sky and it has long been speculated in the City that it would seek to buy full control.

Independent directors of Sky – which is Europe’s biggest pay television broadcaster with 21 million subscribers in the UK, Ireland, Germany, Italy and Austria – have agreed to recommend the offer to shareholders other than 21st Century Fox.

However, the company said that “certain material terms” remained under discussion and that there could be no certainty that an offer would be made by 21st Century Fox.

The announcement follows a rise in Sky’s share price earlier today.

Shares of Sky closed up 210.5p at 1000p – a 26.7% rise on the day. The offer price recommends a premium of 36% to Sky’s closing share price on Thursday evening.

Sky said it had formed an independent committee of its board to consider the American giant’s proposal.

Members include Martin Gilbert, the company’s senior independent director and Jeremy Darroch, the chief executive of Sky.

Mr Gilbert is founder and chief executive of Aberdeen Asset Management, one of the UK’s biggest fund management firms, and a respected City grandee.

Others on the committee include Andrew Griffith, Sky’s chief operating officer and chief financial officer, and Andrew Sukawaty, another non-executive director of Sky and previously chief executive of European satellite operator Inmarsat.

James Murdoch, Sky’s chairman, is not on the committee because he is chief executive of 21st Century Fox.

The deal is likely to ignite a huge amount of debate in the UK media industry.

News Corporation, Rupert Murdoch’s media giant, tabled an £8bn takeover bid in June 2010 for the shares in Sky – then called British Sky Broadcasting – that it did not already own.

That deal attracted a good deal of scrutiny because it would have brought together Sky News with News Corporation’s UK media assets, including The Sun, Britain’s biggest-selling daily newspaper, The Times, The Sunday Times and the News of the World.

This attracted criticism from rivals of those newspapers about a concentration of media ownership and, in response to regulatory concerns, BSkyB agreed to hive off Sky News as a separate company.

However, in July 2011, News Corporation abandoned its offer when it emerged that the News of the World had hacked the mobile phone of murder victim Amanda ‘Milly’ Dowler.

News Corporation subsequently demerged its film and television assets outside Australia into a new company, 21st Century Fox, leaving it as a business focussed on newspaper titles from around the world – apart from the UK titles like The Sun and The Times it also owns the Wall Street Journal, the Australian and the New York Post – and the book publisher Harper Collins.

There are likely to be fewer concerns from rivals of either Sky or the UK newspaper businesses owned by News Corporation about a concentration of the news market.

Sky traces its origins to Sky Television – which was launched by Rupert Murdoch in February 1989.

The business merged with rival satellite broadcaster British Satellite Broadcasting in November 1990 and it floated on the London Stock Exchange in October 1994 in a move that saw News Corporation’s stake reduced to 40%.

However, it retained close ties with News Corporation and 21st Century Fox that, two years ago, saw Sky buy the American company’s interests in Sky Italia and Sky Deutschland to become a pan-European broadcaster.

In an email to Sky’s near-30,000 employees, Mr Darroch said the offer was “the first step in what will now be a formal process over the coming weeks”.

He added: “As you know, 21st Century Fox were the founders of our business and have always been an extremely supportive shareholder and backer of Sky. Many of us have worked closely with them over the years and know them very well.”

Because 21st Century Fox already owns some 39.1% of Sky, buying full control of the company would cost it an estimated £11.25bn.

Speculation has mounted about a possible deal in recent months due to the fall in the pound against the US dollar – reducing the value of Sky, whose shares are quoted in sterling, in dollar terms.