* United Internet to buy KKR's 74.9 pct stake for 586 mln eur
* Deal will raise United Internet's holding to 100 pct
* Purchase indicates shift in strategy
* United Internet shares rise 3.7 percent (Adds synergies, share price)
FRANKFURT, Sept 3 (Reuters) - United Internet agreed on Wednesday to buy KKR's stake in cable group Versatel for about 586 million euros ($769 million) in cash, giving it access to Germany's second-largest fibre optic cable network.
The move indicates a shift in strategy for the German internet service provider, which has until now rented bandwidth and resold it using its 1&1 or GMX brands but has not invested in a grid on its own.
The purchase of the 74.9 percent of Versatel it does not yet control will give United Internet access to a fibre optic cable network that can be accessed in 19 of Germany's top 25 cities.
It will raise United Internet's number of DSL broadband customers to 4.12 million from 3.68 million at the end of June, cementing its position as the country's second broadband provider after Deutsche Telekom.
United Internet said it would keep the Versatel brand and further expand its business with corporate clients.
It also plans to use its cable network to offer DSL connections to its customers, which it said would generate savings of up to 55 million euros a year.
Shares in United Internet rose 3.3 percent to 33.92 euros by 0904 GMT, touching their highest level in more than two months earlier in the session. Germany's technology index was up 1 percent.
Berenberg analyst Usman Ghazi called the deal "a steal" for United Internet. "The multiples are attractive, the synergies are sensible and can be delivered with relatively low risk, and there is strategic rationale," he wrote in a note.
United Internet plans to fund the purchase of KKR's stake in Versatel and repayment of Versatel's 361 million euros of net debt with new loans.
United Internet said accounting changes due to the full consolidation of Versatel would lead to one-time, non-cash income of about 100 million euros in fiscal year 2014, after transaction costs.
Versatel expects to post flat 2014 revenues of about 548 million euros and a 6 percent increase in earnings before interest, tax, depreciation and amortisation (EBITDA) to about 164 million euros.
($1 = 0.76 euro) (Reporting by Maria Sheahan; Editing by Matt Driskill and Georgina Prodhan)