The broadcaster's deal with 21st Century Fox, which is controlled by tycoon Rupert Murdoch, will see it buy all of Sky Italia for £2.45 billion and take a 57.4% interest in Sky Deutschland for £2.9 billion.
The enlarged company will serve 20 million customers and combines the leading pay TV businesses in three of Europe's four biggest markets.
The proceeds will boost 21st Century Fox in its pursuit of Time Warner after it failed with an offer worth 80 billion US dollars (£47 billion) earlier this month.
Twenty-First Century Fox, which will continue to own 39% of BSkyB, includes Fox News and the Fox network behind The Simpsons and Family Guy, as well as Hollywood studio 20th Century Fox, maker of the X-Men and Ice Age films.
The company was formed after Mr Murdoch split it away from the News Corp publishing firm, which controls The Sun, The Times and The Sunday Times, as well as the Wall Street Journal and New York Post.
BSkyB's European expansion was announced at the same time as it said annual operating profits dropped 5% to £1.26 billion due to investments in connected TV services and Premier League football rights.
It ended the year with 11.5 million customers, an increase of 342,000 over the year and 75,000 in the quarter. The company said it added a third more customers than in the previous year, its highest rate of growth in three years.