Christofias was widely believed to have waited too long to respond to the crisis and to curb spending. He was also seen as dragging out negotiations with international creditors and missing the opportunity to secure a bailout earlier.
Anastasiades, who leads the main opposition Democratic Rally party, has boasted of his connections with Europe's center-right leaders and seeks to spend political capital he's built up over the years to convince Europe that Cyprus deserves help.
"When facing great challenges, we want Europe by our side," Anastasiades said.
European Commission President Jose Manuel Barroso congratulated Anastasiades, saying Cypriots had given him "a strong mandate to implement his program of reform and to do what it takes to ensure fiscal and financial sustainability."
Barroso said he spoke to Anastasiades "and I have assured him that he can count on the continued commitment of the European Commission to assist Cyprus to overcome the challenges it faces."
Last year, Cyprus sought financial assistance of up to €17 billion ($22.7 billion), a sum roughly equivalent to its annual gross domestic product, which has raised concerns about whether the country would be able to pay back any loan. The country has been unable to borrow from international markets since mid-2011, and turned to long-time ally Russia for a €2.5 billion ($3.3 billion) loan to keep it afloat in 2012.
But Anastasiades' won't have an easy time negotiating a bailout without possibly more austerity pain for Cypriots, analysts said.
"It will be difficult to resist ... calls for privatizations and he will probably have to agree to sell a stake — ideally for him, not a controlling stake — in profitable government enterprises," Cyprus University political science professor Antonis Ellinas said. "The question is whether lenders think that this would be enough to make the debt sustainable.
"The risk Anastasiades — and foreign creditors — face, is that the new president will quickly lose political capital and become a lame duck long before recovery is in sight."
Cyprus, a divided island of around 1 million people in the far eastern end of the Mediterranean, is one of the smallest members of the 27-nation European Union. Cyprus was divided into a breakaway Turkish-Cypriot north and an internationally-recognized Greek-Cypriot south after a 1974 Turkish invasion triggered by a coup whose leaders wanted to unite the island with Greece. Nicosia is the world's last divided capital.
Anastasiades sent "a message of peace" to Turkish Cypriots, expressing a "sincere intention" to achieve a reunification deal with the support of the EU and "other friendly countries."
Elena Becatoros in Athens contributed.