Prime Minister Antonis Samaras' office made the announcement a day after the banker previously named to the position, Vassilis Rapanos, resigned for health reasons.
Stournaras, 55, is currently the head of the Foundation for Economic and Industrial Research, a think-tank and research body that advises the government. A professor of economics at the University of Athens, he spent several years heading the Finance Ministry's Council of Economic Advisors.
"I do think we have the ability to get past this problem. But we must be realistic," Stournaras said about Greece's financial crisis, speaking at a book presentation shortly before his appointment was announced.
"We have a difficult road ahead of us, an uphill road. But Greece is a country with great potential ... We have to get through a wall — a wall of entrenched attitudes, and those who do not want to hear that Greece has potential. But we will be able to carry it out."
Rapanos resigned Monday from his hospital bed, where he had been since being rushed there following a collapse on Friday. He was discharged Friday.
Rapanos was admitted to hospital before he had time to be sworn in to office, so the title is officially still held by the outgoing minister, Giorgos Zanias.
The finance minister position is a critical one in the debt-struck country, which faces tough negotiations with other European Union countries and the International Monetary Fund as it tries to amend some of the austerity terms of its international bailout.
Samaras himself was convalescing at home after undergoing serious eye surgery to repair a detached retina over the weekend. Doctors have said he must remain home for several days. He is unable to travel to Brussels to attend a European Union summit on Thursday and Friday, but is able to have meetings at his residence.
Greece is sending President Karolos Papoulias to head the country's delegation at the summit, which will also include Zanias.
Samaras heads a three-party coalition government agreed on last week, after a protracted political crisis and two inconclusive general elections since May. He was to meet Tuesday evening at home with the heads of the other two parties in the power-sharing government, socialist PASOK head and former finance minister Evangelos Venizelos and Democratic Left leader Fotis Kouvelis, to discuss the Brussels summit.
Greece, which joined the euro in 2001, has been dependent on two rescue loan deals agreed on with other eurozone countries and the IMF, worth a total €240 billion ($300 billion) for the past two years. In return for the loans, it has imposed harsh austerity measures, including big spending and salary cuts, as well as higher taxes, all in an effort to reform its economy and drastically reduce its borrowings and debt burden.
But the measures have plunged the country into a deep recession, now in its fifth year, and have sent unemployment spiraling to above 22 per cent.
The new coalition government has said it wants to change some terms of the bailout agreement, including lowering some taxes, freezing public sector layoffs and extending by two years the mid-2014 deadline for the austerity measures. Whether it will be able to do this while still receiving bailout funds will depend on how the other EU countries and the IMF view its proposals.
So far they have not received a warm reception. Germany, the largest single contributor to the rescue loans, has insisted Athens stick to its commitments.
Venizelos, who met with Papoulias Tuesday to discuss the EU summit, said Greece remains committed to the EU and staying in the euro.
"The message is that we respect our institutional relationship with our partners," he said after the meeting. "That Greece will not take unilateral actions ... but is asking for an organized review of the (bailout) agreement, as the agreement itself foresees, as European procedures foresee."
Derek Gatopoulos in Athens contributed.