He will remain in custody until Saturday, when a Bulgarian court will decide whether he should be released or held until he is extradited to Serbia.
Ceku is wanted for war crimes allegedly committed during the 1998-1999 war with Serbia when he was military chief of the Kosovo Liberation Army, made up of ethnic-Albanian fighters.
Nikolai Kokinov, a Bulgarian prosecutor, said the Serbian side "must present its case for extradition to the Bulgarian court within a period of 40 days".
Expulsion order
Ceku's arrest comes despite repeated requests from United Nations officials in Pristina, Kosovo's capital, that the Belgrade-issued arrest be disregarded.
Kosovo's government has also asked Interpol and other countries to ignore Serbia's request.
Solomon Pasi, Bulgaria's former foreign minister, said Ceku was coming to the country for an initiative to help Kosovo lobby for Nato membership.
"I am in constant contact and we exchange regular visits with Agim Ceku,'' Pasi said, adding that the warrant for Ceku's arrest was "politically outdated, reflecting realities from a decade ago".
Ceku has been arrested four times, but has never been handed over to Serbian authorities.
Last month, Ceku left Colombia following an expulsion order from the local security agency after Serbian officials asked authorities there to arrest him.
Kosovo's declaration of independence from Serbia in 2008 has been recognised by 60 countries, including Bulgaria, but Belgrade has said it will never recognise an independent Kosovo.