Comcast's initial offer was considerably higher than the Fox bid that valued the satellite broadcaster at £18.5bn.
Sky, based in the United Kingdom, has more than 20 million subscribers in several European countries, in addition to a content arm that includes Sky News.
Fox first went after the 61% of Sky it doesn't already own in December 2016, offering £10.75 per share, but was held up over concerns that the tie-up would give Murdoch too much influence over Britain's media.
However, British regulators have indicated that if Disney succeeds in buying Fox, including the 39 percent stake in Sky, it would be required to offer the same price for the remainder of Sky.
Brian Roberts, chief executive of Comcast, said: "We have long admired Sky, which we believe is an outstanding company and a great fit with Comcast".
Sky shares traded at 14.85 pounds as of 8:14 a.m.in London.
The British government is expected to finally allow Fox, which is run by Rupert's son James, to buy Sky this week, after the USA group agreed to sell Sky's award-winning news channel to Disney to prevent Murdoch from owning too much of the British media.
The battle for Sky between Fox and Comcast is playing out against a larger bidding war between Comcast and Disney for a chunk of Fox's entertainment assets. This values the European pay-TV group at $32.5B, trumping Comcast's earlier $31B (£12.50 per share) offer.
"As the founding shareholder of Sky, we have remained deeply committed to bringing these two organizations together to create a world-class business positioned to deliver the very best entertainment experiences well into the future", Fox said in a statement.
Sky's independent directors accepted the latest Fox offer. After a lengthy review, Disney looks to have satisfied officials with its agreement to sell the 22 regional sports networks included in the deal, allowing the acquisition to progress naturally.