Liberty Global says the deal with Virgin Media means the company will have a total of 25 million customers in 14 countries.
It is already the largest cable operator in most of its 11 European markets. But the majority of revenue is expected to come from five countries - the UK, Germany, Belgium, Switzerland and the Netherlands.
Liberty Global says it plans to continue investing in Virgin's broadband network.
More top news
Watch the amazing moment a cyclist in Russia escapes being killed as a truck and car collide at high speed.
Cameron may have wrong-footed Labour, but there may also be serious rumblings from his own backbenchers, if he wavers on England's future.
Conservative MP Damian Collins believes a recent investigation into corruption at FIFA could result in criminal charges