The purchase of the shares will allow the retail subsidiary to delist from Mexico's stock exchange, in line with the company's interests, a spokesperson told Reuters.
Carso said available stock in Grupo Sanborns will be purchased for 26 pesos ($1.27) per share, a plan Carso's shareholders approved on Monday, according to the statement.
Shares in Sanborns closed Tuesday at 22 pesos on the Mexican stock exchange.
The Slim family already owns 87% of Grupo Sanborns, which also operates Sears department stores in Mexico and El Salvador, while Slim's Inbursa bank owns another 6.7%, according to data from Refinitiv Eikon.
Grupo Sanborns' market capitalization stands at about 50 billion pesos ($2.44 billion).
In Mexico, both the Sanborns chain and Sears stores are upscale retailers.
($1 = 20.4539 Mexican pesos)
(Reporting by Carolina Pulice and Kylie Madry; Editing by David Alire Garcia and Leslie Adler)