Josip Perkovic, sought under a European Arrest Warrant (EAW) which regulates extradition between the bloc's 28 member states, was escorted by police from his Zagreb home to the airport, where he was handed over to German authorities in the early afternoon, state television reported.
He left for Munich aboard a regular Lufthansa flight.
On Tuesday Croatia's Supreme Court said it had rejected Perkovic's appeal against his extradition "as unfounded".
Perkovic, a former Yugoslav secret service agent and Croatia's ex-head of intelligence, has denied any links with the 1983 murder in Germany of Stjepan Djurekovic, a Croatian immigrant who was opposed to Yugoslavia's communist regime at the time.
More From This Section
He was briefly arrested on January 1 after Croatia lifted a limitation it had imposed on extraditions within the EU, but was released two days later pending a final decision on his extradition.
The issue of extradition sparked a row between the EU and Croatia right after the Balkan country joined the bloc in July.
Just days before becoming a member, Croatia changed its domestic law regarding European warrants. The change in the law made it impossible to extradite people wanted for crimes allegedly committed before August 2002, the date the EAW was introduced.
In the wake of the dispute with Brussels, Zagreb amended the law in October.
Local media have speculated that Zagreb was reluctant to extradite Perkovic as he may hold compromising information on influential people in Croatia.
But the government has denied this, saying its aim was to protect veterans of the 1990s independence war from being investigated by the EU.
Since January 1, Croatia has arrested 10 people wanted within the EU.