Interior Minister Dragan Jocic said Lukovic gave himself up outside his home in Belgrade.
Lukovic had been on the run from authorities since Djindjic, a pro-Western reformist, was gunned down by a sniper outside government offices in Belgrade on 12 March 2003.
Lukovic has been on trial in absentia since December, along with other paramilitary and gang figures suspected of involvement in the assassination.
Lukovic, said to be in his late 30s, served in the French Foreign Legion and later led a Serbian paramilitary unit in the wars of the former Yugoslavia in the 1990s. He also led an elite Serbian police unit and is suspected of having led a criminal gang called the "Zemun clan."