Ponta was backed by all members of the opposition coalition, and other parties made no nominations.
Mr Ponta has vowed to fight "injustices" caused by austerity measures of the outgoing cabinet.
Mr Basescu has accused Mr Ponta of trying to interfere with Romania's legal and state institutions.
Mr Basescu, who has been president since 2004, has recently clashed with his rival Prime Minister Victor Ponta.
Mr Ponta, who heads the Social Liberal Union (USL), is himself under pressure to resign over allegations of plagiarism.
Most controversially, Mr Ponta has used his parliamentary majority to suspend Mr Basescu.
New resorts at Ponta do Ouro and Zongoene, where tourists scuba-dive and race four-wheeled motorbikes across sand dunes, are prospering.
"He looks terrible, " Prime Minister Victor Ponta told reporters after visiting Nastase in the hospital, which did not release Nastase's condition.
Situated on a peninsula, Ponta dos Ganchos has 25 villas, which feature private verandas and comfortable hammocks for enjoying panoramic water views.
By 2015 Ponta da Madeira, Vale's private port, will be Brazil's largest by tonnage, exporting 230m tonnes of iron ore a year.
Romania's internal dispute has divided the European political elite, with some social democrats leaping to Mr Ponta's defence, while conservatives react with alarm.
Mr Ponta tried to change the rules on that too, cutting the threshold from half the electorate to a majority of those voting.
Friday evening, President Traian Basescu appointed Social Democrat leader Victor Ponta as the new prime minister with the task of forming a new government.
There was little support for President Basescu before, but the sheer speed with which the Ponta government has moved against him has shocked many.
Victor Ponta risks taking over the role of the black sheep of the European Union from his namesake Viktor Orban, Hungary's conservative prime minister.
Ponta said he will soon announce the members of the new government, which will have to pass a confidence vote in Parliament to be installed.
Victor Ponta became Romania's third prime minister in less than six months when his left-wing-dominated Social Liberal Union (USL) alliance took charge in May 2012.
President Basescu has close links with the centre-right opposition Democrat-Liberal Party (PDL), and Mr Ponta told journalists that trust between the two leaders was "zero".
Prime Minister Ponta says the bibliography lists the papers he consulted.
Mr Ponta may have also misjudged how upset outsiders would be.
They seem to be using Mr Ponta (who has become vulnerable after allegations of plagiarism against him surfaced recently) as an instrument in their power grab.
Claims that Mr Ponta plagiarised 85 pages of his PhD thesis seem to have done him little harm (he fired the academic-integrity body that upheld the charges).
Prime Minister Victor Ponta said the two Romanian slaughterhouses initially suspected to have links to the horsemeat scandal never had direct contact with Comigel and haven't done anything illegal.
Mr Ponta had tried to scrap the requirement of a minimum turnout for the referendum through an emergency decree, but in the face of unusually strong criticism from the EU, he reversed course.
"Victor Ponta has repeated in 10 days what Traian Basescu took eight years to do - the style of governing is rather similar, " said Christian Mititelu, a political commentator in the Romanian capital, Bucharest.
After eight years in office, with strong connections in Europe, and deep loyalty among Romanian journalists, Mr Basescu is winning the information war against a Ponta administration which underestimated the influence of the media.
Why should Mr Orban and Mr Ponta take lectures from an organisation that has been rewriting its own rules on the hoof, tampering with sovereignty without much care for voters and blithely ditching promises made only a few years ago?
"Somewhere in the network to the UK and other countries it seems that something illegal happened and we will fully co-operate to punish any Romanian company involved - but up to now it has not been like this, " Mr Ponta added.
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