Luxury group LVMH and its billionaire CEO Bernard Arnault are set to take full control of Christian Dior.

The French billionaire proposed a €12 billion ($13 billion) deal on Tuesday that was cheered by the shareholders of both luxury titans.

Dior shares trading in Paris advanced as much as 13% to hit a record high, while LVMH shares jumped 4.5%.

The proposed deal is complicated -- but the end goal of the transaction is simplicity.

The Arnault family already owns a controlling interest in both Christian Dior (CHDRY) and LVMH (LVMUY). Arnault is chairman of both firms.

The family is offering to pay a 15% premium for the 26% of Dior they don't already own. The deal would also bring Dior's couture business under LVMH's umbrella.

The "transactions will allow the simplification of the [business] structures," Arnault said in a written statement.

LVMH owns a vast array of high-end brands operating in industries ranging from fashion to perfume and cosmetics. It manages brands including Louis Vuitton, TAG Heuer, Moët & Chandon and Benefit Cosmetics.

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Luxury brands have come under pressure in recent years as sales in the West have slowed or declined.

Allyson Stewart-Allen, a director at International Marketing Partners, said the deal will also help LVMH diversify. Dior's biggest regional market is Asia, accounting for over 30% of its sales.

"It's a risk management strategy to diversify your portfolio ... but it's also about going for growth," she said. "In the emerging markets, Dior is growing."

The companies said they expect the deal to close in the next few months.