Greece's new prime minister, Alexis Tsipras, has picked an outspoken bailout critic as his new finance minister - signalling his resolve to take a tough line with eurozone lenders in an effort to write off a massive chunk of rescue debt.

Economist Yanis Varoufakis, 53 - who has described the bailout as "fiscal waterboarding" - took up the position amid a rating agency warning of a worsening financial situation that sent the country's stock market sharply lower.

The governing Syriza party today announced a Cabinet that includes officials from its coalition ally, the anti-bailout and right-wing Independent Greeks.

Moody's ratings agency described Syriza's election win on Sunday as "credit negative", arguing it would prolong risks to financing, economic growth and bank liquidity.

The agency said it expected the government's "policy uncertainty" to slash 2015 growth to one per cent from the 2.9 per cent predicted in the state budget.

The main stock index in Athens fell on the news, sliding 5.4 per cent before recovering some losses to close down 3.7 per cent amid losses across Europe.

Mr Tsipras won a landmark general election victory after campaigning on a pledge to renegotiate the bailout deal and seek forgiveness of more than half the debt - a message that resonated with voters who have suffered through harsh austerity measures that have included pension and salary cuts.

"We are determined to implement our programme with courage and determination and not take one step back," said senior Syriza official Dimitris Stratoulis, who was appointed deputy minister for state welfare.

Theodoris Dritsas, incoming deputy minister for marine affairs, said the new government would halt plans to privatise more of the country's main port of Piraeus - despite official interest from six bidders for a two-thirds stake.

"Public ownership of the port will remain. The privatisation ... stops here," Mr Dritsas said.

Mr Tsipras chose economist and veteran left-wing politician Giannis Dragasakis as deputy prime minister and expanded powers for the ministries of development, environment, interior and public works - reducing the number of ministries from 19 to 11.

Panos Kammenos, the Independent Greeks leader, was named defence minister.

Finance Minister Varoufakis has been a vocal critic of Greece's bailout agreements, arguing that repayment of the country's huge rescue package loans should be linked to growth, a policy change he argues would benefit eurozone lenders.