MILAN, June 5 (Reuters) - Swisscom's Italian unit Fastweb has agreed to sell its 4.5% stake in Telecom Italia's (TIM) last-mile network business FiberCop to U.S. fund KKR, the Swiss company said in a statement.

KKR will pay 439 million euros ($477 million) for the stake, Swisscom said, in line with the price paid by the U.S. fund to take over TIM's holding in the venture.

KKR is buying Telecom Italia's landline grid, including FiberCop, for an enterprise value of 18.8 billion euros.

Swisscom said it expects to complete the sale of its stake in FiberCop in the third quarter, subject to the expected completion of the KKR-TIM deal in the coming weeks.

($1 = 0.9195 euros) (Reporting by Elvira Pollina Editing by Mark Potter )