The agreed deal reverses Sunrise's failed bid to buy Liberty's Swiss business last year and marks a strategic reversal by the U.S. company which has been divesting European assets.
The all-cash 6.8 billion Swiss franc ($7.43 billion) deal will see Liberty Global, set up by U.S. cable pioneer John Malone, pay 110 francs per share for Switzerland's No. 2 telecoms company, a 32% premium to the company's average share price over the past 60 days.
Sunrise shares rose by more than a quarter to just below the offer price in early trade on Wednesday.
Sunrise's bid to buy Liberty Global's Swiss cable business UPC last year collapsed in the face of opposition from Sunrise's biggest shareholder, Germany's Freenet and activist investors including Axxion and AOC, who baulked at the price.
On Wednesday Freenet, which owns 24% of Sunrise, committed to tender its shares for Liberty Global's bid.
"It's a fair valuation," Freenet CEO Christoph Vilanek told Reuters. "We believe that a merger on sensible terms makes sense."
The deal, which is subject to regulatory approval, is the latest sign of consolidation in the telecom industry as companies try to cut costs and ramp up investments in technology.
Liberty Global said it approached Sunrise in July with the proposed offer and got a positive response.
"I've always said the market requires rationalisation and we remain opportunistic about strategic developments there," Liberty Global Chief Executive Mike Fries told reporters. "The industrial logic of this deal is undeniable."
In Switzerland Sunrise and Liberty Global trail state-controlled Swisscom, the dominant provider of internet, mobile phone and cable TV services.
Together, the combined business would have 3.17 billion Swiss francs in revenue, 2.1 million mobile subscribers, 1.2 million broadband subscribers and 1.3 million TV subscribers, reflecting approximately 30% market share in each segment, Liberty Global said.
PUTTING CAPITAL TO WORK
Liberty had been divesting European assets on a view that the sector is expensive in light of its high capital costs and low growth prospects.
The biggest deal, the sale of its cable networks in Germany and central Europe to Vodafone, netted $22 billion last year.
Fries said Liberty Global had pulled out of Austria and Germany because its operations there lacked scale, while elsewhere it was looking to expand its footprint.
In Belgium it bought a mobile operator, while in the Netherlands and UK it was creating joint ventures, he said.
Liberty's takeover of Sunrise follows the 24 billion pound ($31.32 billion) tie up between Liberty Global's Virgin Media and Telefonica's O2 and the taking private of Spain's Masmovil by private equity investors.
Fries said Liberty Global wanted to use its strong balance sheet.
"We are sitting on $10 billion of liquidity right now," he said. "We felt this is a great market and a great opportunity to put capital to work."
Credit Suisse, JP Morgan and LionTree acted as financial advisers to Liberty Global while Homburger and Shearman & Sterling provided legal advice.
Deutsche Bank acted as financial adviser and Lenz & Staehelin as legal adviser to Sunrise.
($1 = 0.9157 Swiss francs)
($1 = 0.7664 pounds)
By John Revill