The companies will create a 50-50 joint venture, they said in a joint statement.
Vodafone, whose Dutch operations are worth a bit less than those of Liberty Global, will make a cash payment of EUR one billion to the American firm to equalize ownership in the new company.
With more than 15 million customers it will be the second largest telecoms company in the Netherlands, after KPN.
The companies forsee synergies of EUR 280 million per year and EUR 3.5 billion altogether, when cost reductions are taken into account.
Liberty Global's activities in the Netherlands include cable operator Ziggo, which it acquired in 2014 for EUR 10 billion.
Ziggo's stake of the high speed Internet market in the Netherlands is 44 percent, according to ABN Amro. KPN is next with 40 percent.
Liberty Global's Dutch operations are valued at EUR 14 billion. They posted revenue of EUR 2.5 billion last year.
Vodafone has a market value of EUR 4.7 billion in the Netherlands, and is far behind KPN and Ziggo in both television and cable. It posted revenue of EUR 1.93 billion in 2015.
The transaction is due to close late this year and needs approval from anti-trust regulators. It could speed up telecoms mergers in Europe.
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