Rupert Murdoch's 21st Century Fox already owns 39% and he first tried to buy the remainder five years ago before abandoning the attempt in the wake of the phone-hacking scandal.
Martin Gilbert, the chairman of the independent directors (which excludes James Murdoch, who is unable to vote because of his role as chief executive of Fox), recommended the deal today saying it delivered good value for shareholders.
Not all of them agree with Gilbert. One shareholder told the BBC, "this is a patsy deal. Many of the directors are not really independent and as a group they should be ashamed of themselves"
The BBC understands that James Murdoch, Rupert Murdoch's son and chief executive of 21st Century Fox, met with directors in early December and told them "we are either a buyer or seller of our stake. The status quo is not an option".
James Murdoch offered a 30% premium to the existing price on the condition the directors recommended it. After further meetings, that premium was raised to 40%.
Even with that premium, the sale price is roughly what the company was worth six months ago and many shareholders will feel short-changed.
The directors felt that if Fox had pursued a hostile bid, it could have bought shares in the open market at the prevailing price to take its 39% stake to more than 50%. After making an offer for the remaining shares, Sky shareholders may have ended up with a lower premium of around 20-25%.
Fox will require 75% of the independent shareholders to approve the deal. It may also be referred to regulators to check whether it breaks national interest tests on the plurality of media.
The Secretary of State for Culture Media and Sport, Karen Bradley has 10 days to decide whether to take that option.
Given the outcry over the last bid, it seems likely she will do that but the media landscape has changed a great deal since the last takeover attempt.
The last bid came from NewsCorp, which owns the Wall Street Journal, The Times and The Sun. This bid is from Fox which owns television and film businesses.
The emergence of new players in media like Netflix and Amazon mean that this deal would mean less concentration of power in the sector.

Ben Blakeley, the ex-boyfriend of the pregnant 17-year-old, strangled and buried her in his uncle's grave in Didcot, Oxfordshire, in December 2013.
He admitted affray in connection with an incident at Didcot Parkway station on 22 October 2013.
Blakeley, 23, from Reading, was given a concurrent eight month sentence at Oxford Crown Court.
He was jailed for life in July last year for the murder of Jayden.
Jayden was last seen alive on 3 December. Her body was discovered two weeks later on 18 December in a recently disturbed grave at All Saints' Church in Didcot.
Blakeley's brother Jake, 18, of Abbotts Road, Didcot, was jailed for three years for perverting the course of justice.
Sky's independent directors have recommended a takeover offer from 21st Century Fox valuing the company at Â£18.5bn.
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A man who is serving life for murdering teenager Jayden Parkinson has been given a further sentence for affray.