Ziggo, which in October rejected an earlier offer from Liberty, said in a joint statement on Monday that the current offer implied a price of 34.53 euros per share compared with Friday's close of 33.25 euros.
Liberty, controlled by U.S. tycoon John Malone, has built its leading position in a broad stretch of Europe from Ireland to Romania via acquisitions over the past decade. It already owns 28.5 percent of Ziggo.
Buying the rest will increase Liberty's presence in the Belgium and the Netherlands, where it also owns Ziggo's Dutch competitor UPC, as well as a majority stake in Belgian group Telenet, the main cable group in the north of Belgium.
Under the terms of the deal, Liberty Global will pay a stock dividend of one class C share for each existing class A, B or C share in early March.
Upon completion of this, Ziggo shareholders will receive 11 euros in cash, 0.2282 Liberty class A shares and 0.5630 class C stock, 74 prior to completion of the stock dividend) for each Ziggo share that they hold.
The offer represents a 22 percent premium to the closing share price of Ziggo on Oct 15, 2013, the day before Ziggo announced it had received a preliminary proposal from Liberty.
Follow us on Twitter: @CNBCWorld