Yanis Varoufakis is an outspoken critic of the conditions imposed on Greece in return for the 2010 bailout.
He will have the tough job of leading talks with the EU over the Syriza party’s pledge to renegotiate Greece’s massive international bailout.
Panos Kammenos is a member of the anti-bailout Independent Greeks party.
It joined a coalition with Syriza, after the left-wing party narrowly failed to secure a majority in parliament in Sunday’s elections.
The EU has meanwhile warned that the new government must stick to its creditor commitments.
The government’s chief economics spokesman, Euclid Tsakalotos, has argued that it is unrealistic to expect Greece to repay its huge debt in full.
Correspondents say that the appointment of Yanis Varoufakis – who holds dual Greek and Australian nationality – is a signal that the new Syriza-led coalition will take an uncompromising stance when renegotiating Greece’s €240 billion ($270 billion) EU-IMF package.
Yanis Varoufakis insists that Greece cannot restore its finances until its debt is lessened and has described the bailout as “fiscal waterboarding”.
Before the appointment of Yanis Varoufakis, PM Alexis Tsipras said EU leaders needed now to show that they were willing to work with Syriza – and that it would be his “worst nightmare” if the eurozone collapsed because Greece fell.
The appointment of Panos Kammenos into the 11-minister cabinet is also likely to be controversial, correspondents say, because of his claims that Germany is to blame for his country’s economic woes by its insistence on budgetary belt tightening.
Other key appointments made by the prime minister include: Nikos Kotzias as foreign minister, Nikos Pappas as state minister, Nikos Voutsis as interior minister, Panagiotis Lafazanis as production and environment minister, Panos Skourletis as labor and social solidarity minister.
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