Sophie Lacoste Dournel, who was named non-executive chairman in September, was locked in a feud with her father, Michel Lacoste, who opposed her nomination and had already agreed to sell his 30.3 percent-stake shares to Maus.
Until then Maus, a holding company whch owns the Manor department store chain in Switzerland, had controlled 35 percent.
Lacoste Dournel issued a statement saying she and allied shareholders had agreed to cede their 28 percent of the capital to Maus -- though she described the decision as "extremely painful" at a press conference.
"After studying several options, Sophie Lacoste Dournel and the family shareholders she represents have accepted that any action that pitted two groups of shareholders against each other would harm the interests of the firm and its employees," the statement said.
"As a result they have agreed to sell their shares to the Maus Frères group."
The move will hand Maus 93.3 percent of the firm's capital.
"It is with great sadness that we will cede our share in the company that my grand-father created," Lacoste Dournel said.
Michel Lacoste had accused the Swiss group of seeking to split his family and of manipulating his daughter to gain control of the brand.
But late last month he changed tack, agreeing to sell his own shares to Maus.
Last month's sale valued Lacoste at between one and 1.25 billion euros ($1.6 billion).
Lacoste Dournel said the upcoming transaction would be carried out on the same basis, with her 28 percent worth between 280 million and 350 million euros.
The iconic Lacoste brand was founded in 1933 by tennis champion René Lacoste, and posted 2011 sales to retailers of 1.6 billion euros ($2.1
Its business model is based on licences sold to companies which then pay royalties to the group.
Maus, which once owned the Printemps department store in Paris, owns several Swiss shopping centres, the Fly furniture chain and Manora restaurants, among other interests.