The world's largest retailer says the change will take effect at the end of its annual meeting today.
Walton, son of Wal-Mart founder Sam Walton, has been chairman since 1992. The company says the 70-year-old will continue to serve as a director.
Penner, 45, joined Wal-Mart as a management trainee and held a number of positions including senior vice president of finance and strategy for Walmart.Com and chief financial officer for the Japan unit. He joined Wal-Mart's board in 2008. Rob Walton noted on stage at the meeting that Penner is married to his daughter.
Wal-Mart Stores Inc. Is based in Bentonville, Arkansas.
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