LONDON--British pay- and satellite-television giant British Sky Broadcasting Group PLC said Friday it agreed to buy all of Sky Italia and most of Sky Deutschland AG from Rupert Murdoch's 21st Century Fox, for about GBP5.35 billion ($9.09 billion), mostly in cash.

BSkyB will buy Fox's 100% stake in the Italian TV company for GBP2.45 billion, GBP2.07 billion of which will be in cash. BSkyB will also transfer its 21% stake in the National Geographic channels to Fox, at a value of GBP380 million.

BSkyB will also buy the 57.4% of the German business that 21st Century Fox owns. It said it would pay GBP2.9 billion in cash for that stake, valuing Sky Deutschland at EUR6.75 ($9.09) a share. BSkyB is also offering EUR6.75 a share to the remaining minority shareholders in Sky Deutschland, intending to take full ownership of the company.

The deal is subject to regulatory and shareholder approval. While there are no clear regulatory hurdles, price may be an issue for shareholders on both sides. Fox is BSkyB's biggest shareholder, holding a 39.1% stake. BSkyB's other shareholders will need to be convinced the stakes are adequately valued.

Shareholders seemed skeptical in early European trading, with BSkyB shares down 2.8% to 899 pence and Sky Deutschland shares up 2% to EUR6.80, above BSkyB's offer price.

The deal stands to help BSkyB battle earnings erosion after spending heavily on technology upgrades, programming and premium sports-TV rights. For Mr. Murdoch, it provides a bulk of cash as 21st Century Fox weighs a takeover bid for Time Warner Inc.

21st Century Fox was until June 2013 part of the same company as News Corp, publisher of The Wall Street Journal and Dow Jones Newswires.

Write to Simon Zekaria at simon.zekaria@wsj.com and Rory Gallivan at rory.gallivan@wsj.com

Subscribe to WSJ: http://online.wsj.com?mod=djnwires