LONDON — Comcast emerged as the victor for the British broadcaster Sky on Saturday, beating 21st Century Fox in a monthslong battle whose outcome promises to reshape the media landscape.

With a final offer that values Sky at about 29.7 billion pounds, or roughly $39 billion, the American cable giant wrested away control of Sky from Rupert Murdoch and the Walt Disney Company, which is buying most of Mr. Murdoch’s company, Fox.

The final battle for control of Sky, a pay-television company whose reach extends across Europe, came down to an unusual one-day, three-round auction overseen by Britain’s Takeover Panel. At the end, Comcast bid £17.28 per Sky share, while Fox had bid £15.67 a share.

Comcast and its chief executive, Brian L. Roberts, have succeeded in an international foray into empire building, gaining a big European outpost. Sky also represents yet another source of content that could prove valuable as traditional media and telecommunications companies vie against Netflix. While Comcast already owns NBCUniversal, more original shows and sports programming rights could help retain existing subscribers and draw new ones.