Terms weren't disclosed, but German press reports said the purchase price was around 860 million euros.
Audi CEO Rupert Stadler cited Ducati's "great expertise in high-performance engines and lightweight construction" as a factor underpinning the acquisition.
Ducati will be the third Italian brand within the VW Group, next to super sports car maker Lamborghini and the Italdesign studio.
In 2011, Ducati had revenue of 480 million euros. The company, which was founded in 1926, sold 42,000 motorcycles.