Cvitanich signed for Ajax, although he did not leave Banfield until the end of the 2008 season. He was labelled the successor to Klaas-Jan Huntelaar and scored his first goal against NAC Breda on 12 December 2008. Following the match against NAC, Cvitanich scored his first brace and his first hat-trick in subsequent weeks against De Graafschap and ADO Den Haag. He scored his first hat-trick of the 2009–10 season against NAC Breda.
Cvitanich obtained the Croatian passport back in 2008, but that's not a sufficient argument for the FIFA.
Cvitanich obtained a Croatian passport in August 2008. He has dual citizenship, holding both Argentinean and Croatian passports. The surname Cvitanić has his origin on the island of Brač. During the last century, every tenth citizen of the island was one of the family of the Cvitanić's.