UPDATE 2-France's Orange to sell remaining stake in Britain's BT

* BT to buyback up to 80 mln pounds of Orange shares

* Orange to offer about 248 mln shares, or 2.5% stake

* Orange stake worth 493 mln pounds or 550 mln euros (Recasts, adds context on BT revamp, Orange's recent performance)

By Justin George Varghese

June 27 (Reuters) - BT Group said on Thursday its third-biggest investor Orange would sell its remaining 2.5% stake, valued at over $600 million, in the former British telecoms monopoly.

BT said it intended to repurchase up to 80 million pounds of shares offered by Orange. The French group said it would offer approximately 248 million shares to eligible institutional and qualified investors.

Orange gained the stake when BT bought mobile operator EE, which was a joint venture between the French company and Germany's Deutsche Telekom, in 2016.

At closing prices, the French former monopoly's stake is worth 493 million pounds ($625 million), or around 550 million euros, according to a Reuters calculation.

The stake sale comes as BT undergoes a major restructuring under new chief Philip Jansen.

Orange is battling a tough competitive environment back home where rivals are engaged in a race to win market share.

Orange's rivals Altice Europe, Bouygues Telecom and Iliad are all controlled by billionaires who have failed to consolidate their position in the market through mergers over the past few years.

NO MORE BT EXPOSURE

After the stake sale the French rival said on Thursday it will no longer be a shareholder of BT and will no longer have any exposure to the company's shares, having recently fully hedged its exchangeable bonds into BT shares issued in June 2017.

Orange, which held a 4% stake in BT after the sale of EE in 2014, trimmed a third of its exposure in 2017 when the British firm suffered what it called a "challenging year."

BT's shake-up, which includes 13,000 job cuts, was announced a year ago and aims to tackle problems ranging from criticism of BT's fibre broadband to an underperforming IT services business.

BT's largest shareholder Deutsche Telekom holds a stake of about 12%, which is also a legacy of BT's 12.5-billion-pound acquisition of EE.

BT said it intends to hold the shares acquired in the repurchase, adding that the offer price and final number of shares sold will be determined by Orange at the conclusion of the bookbuilding process.

"The repurchase is expected to settle on July 2," BT said.

Citigroup Global Markets Limited is acting as sole bookrunner for the share placement. ($1 = 0.7893 pounds) (Additional reporting by Sarah White in Paris; editing by David Evans and Elaine Hardcastle)