Bernard Arnault is the boss of LVMH, which runs Louis Vuitton and Moet champagne, and is also the main shareholder in Christian Dior.
Under the complex deal, the Arnault family will offer to buy the rest of Dior that it does not already own.
LVMH will also buy Dior's high-end fashion line for 6.5bn euros (£5.5bn).
That will unite Christian Dior Couture, the 70 year old fashion label which has been worn by film stars from Elizabeth Taylor to Jennifer Lawrence, with the Christian Dior perfume and beauty business already owned by LVMH.
The move was welcomed by investors, who have called for Mr Arnault to simplify the structures of LVMH and Dior.
Shares in Christian Dior jumped about 11% and LVMH shares rose 5.4% on Tuesday.
Mr Arnault said the move would be an "important milestone" and underlined the confidence of his family group in LVMH.
"The corresponding transactions will allow the simplification of the structures, long requested by the market, and the strengthening of LVMH's Fashion and Leather Goods division thanks to the acquisition of Christian Dior Couture, one of the most iconic brands worldwide," he said.
Christian Dior Couture, which almost exclusively sells its goods through its 198 high-end stores, had revenues of more than 2bn euros last year and profits of 270m euros.
Mr Arnault has a fortune of nearly $51bn (£40bn), according to Forbes.
As well as LVMH and Dior, he also owns stakes in French luxury goods rival Hermes and supermarket chain Carrefour.
LVMH, which was created through the merger of Louis Vuitton and Moet Hennessy, owns more than 70 brands worldwide. They include:
France's richest man has made a £10bn move to combine the Christian Dior fashion house and luxury goods firm LVMH under the same ownership.