It offered a £17.28 share price for the British TV broadcaster against Fox’s £15.67 in a sealed auction.
The deal will spark the largest takeover seen in Europe’s media industry.
Comcast will now become the biggest pay-TV provider in the world, with around 52million customers.
UK regulator The Takeover Panel set up the auction to end a transatlantic bidding battle which has waged since February.
Comcast initially gatecrashed a takeover of Sky from Fox, which already owns 39 per cent of the company.
The auction began on Friday after the London stock market closed — and went the maximum three rounds.
The result is a setback for US entertainment giant Walt Disney, which would have taken ownership of Sky if Fox won.
It agreed a separate £54billion deal to buy the bulk of Fox’s film and TV assets, including the Sky stake, in June.
Sky is Europe’s largest pay-TV operator, with 23million customers in seven countries.
Shareholders will still have to vote on the deal but its independent directors are expected to recommend Comcast’s bid.
Comcast chief executive Brian Roberts hailed a “great day”, adding: “We couldn’t be more excited by the opportunities in front of us.”
Sky chief Jeremy Darroch said: “Sky has never stood still, and with Comcast our momentum will only increase.”
Rupert Murdoch, chairman of News Corp, owner of The Sun, is also co-chairman of 21st Century Fox, with son Lachlan.
His son James is chief exec of 21st Century Fox and Sky chairman.
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