The company said it expects Simons "will propel its iconic style into the 21st century."
Galliano was fired last year after he made anti-Semitic remarks during an altercation in a cafe. Blaming his behavior on job stress and addictions to Valium and alcohol, he checked into rehab, but still lost his position at Dior.
The New York Times said Simons' first collection for Dior will debut in July in Paris.
"The first time I heard about the Dior position, I thought, 'This feels right,'" the Times quoted Simons as saying.
The 44-year-old designer previously worked for the Jil Sander label. He has run a separate men's wear business in Antwerp since the mid 1990s, the newspaper said.