Mr Leighton had long been tipped for the role, which puts him in charge not just of Asda's 231 stores but also Wal-Mart's continental European operations. These include 95 outlets in Germany acquired from Wertkauf and Interspar.
Analysts had speculated that Mr Leighton might leave Asda if he did not gain a wider role within Wal-Mart.
The business has already lost Archie Norman, who has stepped down as chairman to concentrate on other interests, including his investment in Knutsford, the shell company that is seeking a retail takeover.
News of the appointment came as Wal-Mart announced that its underlying sales in the four weeks to 26 November had risen by 5.6 per cent. The main Wal-Mart stores performed strongly with sales up by 6.4 per cent if new space is stripped out. But the figures was diluted by the Sam's Club membership outlets where underlying sales were up by just 2.5 per cent.
The company said that by the end of November it had 1,803 discount stores, 682 supercentres and 457 Sam's Clubs in the United States.
Separately Asda yesterday unveiled a deal with German television and hi-fi manufacturer Schneider Rundfunkwerke, which is already a key partner of Wal-Mart in Germany.
The deal is worth pounds 60m in the first year and aims to bring consumer electronic goods at low prices to the UK in the next 12 months.
A 14-inch television and Nicam video manufactured by Schneider were on sale at Asda yesterday with prices starting at pounds 79.99.