By Foo Yun Chee and Elvira Pollina

BRUSSELS/MILAN (Reuters) -U.S. investment firm KKR secured unconditional EU antitrust approval on Thursday for its up to 22-billion-euro ($24 billion) acquisition of Telecom Italia's (TIM) fixed-line network.

The deal is significant as it marks the first time that a former phone monopoly in a major European country is divesting its landline grid.

The European Commission's announcement confirmed a Reuters' story last week.

"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," the EU executive, which also acts as the EU antitrust watchdog, said in a statement.

TIM shares turned positive and closed Thursday's session 1.5% higher, reversing earlier losses following the Commission statement.

KKR has sought to address concerns of Telecom Italia's rivals about those rivals' existing contracts put in place after the creation of FiberCop, Telecom Italia's last-mile grid unit, and has offered a pledge to keep them on the same terms and prices, people with direct knowledge of the matter have told Reuters.

This informal remedy has also allayed EU worries, they said.

The Commission said a master services agreement (MSA) that will govern the relationship between NetCo (the grid acquired by KKR) and TIM post-transaction is not an integral part of the transaction, as it is not an agreement through which KKR acquires control over NetCo.

The network sale is part of a government-backed plan aimed at cutting TIM's heavy financial burden. The EU's green light will now allow the deal to be finalised shortly, Italy's Economy Minister Giancarlo Giorgetti said in a statement.

($1 = 0.9245 euros)

(Reporting by Foo Yun Chee and Elvira Pollina, additional reporting by Giuseppe Fonte in Rome; Editing by Susan Fenton)