While a price for the transaction has not been revealed, Reuters' sources have suggested the deal cost Audi about 860 million euros ($1.08 billion).
Audi's parent company, Volkswagen Group, will be keen to take advantage of Ducati's extensive know-how in small-capacity lightweight motors.
Chairman of the Board of Management of Audi AG Rupert Stadler said of Ducati, "It has great expertise in high-performance engines and lightweight construction … [making] Ducati an excellent fit for Audi."
Audi will now add Ducati's 1100 employees and manufacturing facilities in Bologna and Thailand to its eight existing plants in Germany, Hungary, China, Belgium, India, Slovakia and Spain.
Reactions to the sale have been mixed with some questioning how strongly the acquisition favours Audi, especially considering Ducati's rumoured 200 million euro ($255 million) debt was part of the deal. Stefan Bratzel, director of the Center of Automotive at the University of Applied Sciences in Bergisch-Gladbach, told Reuters, "Ducati doesn't enhance Audi's business model in any way, it's just a trophy in the wall cabinet."
Ducati was founded in Bologna, Italy in 1926 by Adriano and Marcello Ducati and initially built parts for radios before starting to manufacture motorcycles in 1949.
Ducati is currently competing in both MotoGP and World Superbikes.