Fico's Smer party won a majority in parliament and the prime minister in waiting said he would uphold the outgoing government's commitment to cut the country's budget gap and support steps to strengthen the eurozone.
A government led by the 47-year-old europhile, who was prime minister between 2006 and 2010, will please Slovakia's partners. They were upset by a refusal by the outgoing centre-right coalition to contribute to the first bailout of Greece and the delaying of plans to beef up a rescue fund for troubled countries.
"The European Union can lean on Smer because we realize that Slovakia, as a small country living in Europe and wanting to live in Europe ... desires to maintain the euro zone and the euro as a strong European currency," Fico said at his party headquarters, to the cheers and applause of supporters.
The former lawyer's sweeping victory knocks the SDKU-led coalition of Mikuláš Dzurinda from power in the early election, called after the cabinet fell apart in a row over the euro rescue fund last October after just 15 months in office. It has been acting in an administrative capacity since then.
Final, unofficial results showed Smer, a social democrat party, took 44.4% of the vote on Saturday, giving it 83 of parliament's 150 seats.
Damaged by allegations of graft, Dzurinda's party won just 6.1%, less than half of what it won in 2010. But it avoided being knocked out of parliament altogether by clearing a required 5% threshold.
The margin of victory is unprecedented for any party since Slovakia split from its former federation partner, the Czechs, in 1993.
It also resembles the sweeping win by Hungary's centre-right Fidesz party of Viktor Orbán against a discredited left in 2010. Some pundits say there are similarities between Fico and Orbán because both have harangued the press and passed controversial media laws, and have criticised foreign-owned companies operating in their countries.
President Ivan Gašparovič said he would ask the head of the winning party to lead talks on forming a government.
Fico said he would seek a coalition partner but it is likely he will end up ruling alone given Smer's majority. That would be Slovakia's first single-party government since the 1989 end of communism.
Changes in fiscal policy: taxing the rich
Fico says he plans to continue the outgoing cabinet's work to protect the country's sovereign credit rating and cut public spending, although he allowed deficits to swell at the height of the economic crisis in 2009-2010.
The country of 5.4 million people, which has maintained more investor confidence than other peripheral eurozone states, has budget deficit targets of 4.6% of gross domestic product this year and below 3% in 2013, the EU's official limit.
But Fico has vowed to dump Dzurinda's flagship policy - a 19% flat income tax - and reel in more from the rich, banks and other firms that have enjoyed high profits.
"We don't want to go only the way of cuts and savings ... We want to raise taxes on the rich and strong. We will not touch Slovaks with lower incomes," Fico said on Sunday.
Fico's plans involve almost doubling a tax on bank deposits to 0.7%, raising corporate tax to 22% from 19%, and raising income tax for those earning over €33,000 per year.
Fico, who wields near unrivalled power within Smer, has also criticised reforms by the previous government that made it easier to hire and fire workers. That struck a chord among voters afraid of job insecurity in the eurozone's second-poorest country, where 13.7% are unemployed.
The minimum monthly salary is just €327, half that of crisis-hit Greece.