“The deal will be completed as soon as possible after it is cleared by the authorities,” Audi said in a statement.
It did not give financial details but press reports put the price at around 860 million euros ($1.12 billion).
The deal will give Volkswagen an entry into the top-end motorcycle market, taking on its auto rival, BMW.
Ducati, established in Bologna, northern Italy in 1926, is famous for its high-speed road and racing bikes, of which it sold 42,000 last year worth 480 million euros.
Investindustrial, an investment fund, has controlled the company since 2006 with a 70 percent stake.