MEXICO CITY--Companies controlled by Mexican telecommunications tycoon Carlos Slim said Friday that they plan to buy back AT&T Inc.'s 8.27% stake in Mr. Slim's wireless behemoth América Móvil.

AT&T, a longtime investor in América Móvil and its forerunner Telmex, alerted the market in May of plans to unload the roughly $6 billion stake to facilitate regulatory approval of its $49 billion purchase of DirecTV, which competes with Mr. Slim's company in pay television in Latin America.

América Móvil said in a statement that its board of directors approved plans by Inmobiliaria Carso and a subsidiary to purchase 5.74 billion of América Móvil's AA shares, which represent 23.8% of the company's voting shares and 8.27% of América Móvil's equity.

Mr. Slim's companies will also buy 72.8 million of América Móvil's limited voting, or L shares, from AT&T, América Móvil said.

The intervention of Mr. Slim's companies ensures that the billionaire will retain control of the wireless firm without stretching América Móvil's balance sheet. After an acquisition binge in Europe, América Móvil's net debt at the end of March stood at around $33.6 billion, equivalent to 1.6 times earnings before interest, taxes, depreciation and amortization.

AT&T began reducing its holdings in the Mexican company in the open market last year, selling $320 million worth in the first quarter after selling $1.2 billion in 2013.

Once Mr. Slim's buyback plan has been executed, AT&T will no longer be an América Móvil shareholder, the company said.

In announcing the plan, América Móvil said it "recognizes the great value that the association with AT&T brought to both sides over more than 20 years."