In a parliament debate that dragged into the night, Ivica Dačić dismissed concerns in the West that Serbia might veer from the pro-European Union path set by reformers who ousted Milošević 12 years ago and who now find themselves back in opposition.
But the Socialist party leader said he would not deal anymore with his country's dark past.
"If they say the word Balkan means 'blood and honey', there's been enough blood, it's time to feel the taste of honey too," the 46-year-old prime minister-designate told the assembly.
"Serbia is offering the hand of reconciliation, to all. Let's not deal anymore with the past, let's deal with the future."
The West is closely scrutinising Dačić's ascent to the post of prime minister, in an alliance with the nationalists of Serbian President Tomislav Nikolić, for any sign that Serbia may drift from the path chosen by the entire ex-Yugoslavia to join the EU.
The two last shared power at the close of Milošević's disastrous 13-year rule, when his forces expelled hundreds of thousands of majority ethnic Albanians from Kosovo and NATO bombed for 11 weeks in 1999 to wrest the province from him.
Dačić was Milošević's spokesman, railing against the West. He now says Serbia's future is in the EU, but Western diplomats admit to deep unease over whether he is really committed to the political and economic reforms it will take.
His government inherits an economy sliding into recession, an unemployment rate of 25.5% and a shrinking, ageing population that scrapes by on an average net monthly wage of €340. The dinar has hit a succession of record lows against the euro on investor uncertainty over the policy of the new government.
"A key goal of this government will be the acceleration of European integration and maximum effort to secure a date for the start of accession talks," Dačić said.
A vote on his cabinet had been expected on Thursday but the heated debate ran into Friday.
Kosovo was Milošević's last throw of the dice, after fomenting wars in Croatia and Bosnia that killed some 125,000 people as federal Yugoslavia fell apart. He died in 2006 in a cell in The Hague, on trial for genocide and other war crimes.
The Kosovo question
The West says Serbia's progress towards EU membership rests on it coming to terms with the loss of Kosovo, an impoverished territory steeped in history and myth for many Serbs but recognised by almost half the world as independent.
Dačić said he was ready to continue EU-mediated talks with Kosovo aimed at "normalising life for all citizens". But Serbia would never recognise it as independent, he said.
The EU says it won't have to, at least explicitly, but it will have to loosen its grip on a Serb-populated slice of Kosovo's north, and stop obstructing the country's development.
Dačić's cooperation on Kosovo will determine how quickly the EU opens accession talks with Serbia, which became an official candidate for membership in March.
Opposition lawmaker Nenad Čanak, a sharp-tongued critic of the Socialists, said the past would not be forgotten so easily "like it was some boring past of minor bickering over interest rates, and not a Balkan quagmire of five wars and hundreds of thousands of dead and displaced."