Serbian law would allow Kalinic to request a retrial, although it is not yet clear he will use that right.
Kalinic was a member of the so-called Zemun gang, Serbia's single largest organised crime ring in early 2000s.
The gang, along with disgruntled nationalists, had plotted to kill Djindjic after he announced his determination to tackle organised crime in the country.
"With this extradition we will shed light on many unresolved killings," Miljko Radisavljevic, a Serbian prosecutor, said.
It is the first extradition since the two countries signed an agreement last June allowing the extradition of organised crime and corruption suspects between the two nations.
The fight against organised crime and corruption is a major requirement from the European Union for any countries joining the bloc.
Croatia hopes to complete EU entry talks early next year, while Serbia applied for EU membership last year but has not yet started accession talks.