The deal marks the first time that a former phone monopoly in a major European country is divesting its landline grid.
"The Commission investigated the impact of the transaction on the market for wholesale broadband access services in Italy and concluded that it would not significantly reduce the level of competition," an EU executive, said in a statement.
The network sale is part of a plan by the Italian government-backed TIM, aimed at cutting its heavy financial burden.
The greenlight will allow the deal to be finalised soon according to Giancarlo Giorgetti, Italy’s economic minister.
KKR, meanwhile, has been seeking to address concerns from TIM’s rivals about existing contracts already in place after the inception of FiberCop, TIM’s last-mile grid unit.
The US investment firm has pledged to keep them on the same terms and prices according to Reuters.