The 50-year-old former general was arrested at a hotel in the Canary Islands on Wednesday night and flown from Tenerife to a Spanish military base in southern Madrid before being transferred to the Netherlands.
He'll be tried by a UN tribunal for the murder of 150 Serbs and the expulsion of tens of thousands more from their destroyed villages.
Gotovina was ranked third on the tribunal's list of wanted fugitives.
Many Croatians regard Gotovina as a war hero, and thousands have attended a rallies in Zagreb and Zadar, demanding that he be tried in Croatia and calling on their government to provide legal assistance for him.
Croatian police reported more than a dozen protests involving roadblocks, fires and arson attacks on cars.
Croatia's help in finding Gotovina helped clear the way for membership talks with the European Union.