The cash and stock deal - which Liberty Global said is valued at $23.3bn (£15bn) - is subject to approval by shareholders.
The transaction is equal to $47.87 (£30.57) per Virgin Media share, the companies said.
It comes as Virgin Media, which is listed in New York but has a secondary listing in London, said its operating income for the year to the end of December was £699m - up from £540m in 2011.
The company - in which Sir Richard Branson owns a 3% stake - said its cable customers had increased by 88,700 over the last year.
Liberty Global is owned by billionaire media mogul John Malone, and already has a strong presence in Europe.
The US cable group said the merged company would have 25 million customers in 14 countries.
Mr Malone had previously said he would like to enter the UK market and had looked into buying Virgin Media before.
Following news of the deal, Liberty Global's chief executive Mike Fries said it would keep Virgin Media's current strategy and content, and would continue to invest in its broadband network.
He added: "Virgin Media will add significant scale and a first-class management team in Europe's largest and most dynamic media and communications market.
"After the deal, roughly 80% of Liberty Global's revenue will come from just five attractive and strong countries - the UK, Germany, Belgium, Switzerland and the Netherlands."
Virgin Media, whose chief executive Neil Berkett said he would step down if the merger goes through, will continue to operate under this brand in the UK.
Almost five million households in the UK subscribe to Virgin's broadband, television and landline services, and it has around three million mobile phone customers in Britain.
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