Greece will go to the polls again on June 17, just weeks after a first general election produced stalemate.
The announcement follows a meeting of party leaders with President Papoulias on Wednesday morning.
He has now named a senior judge as interim prime minister with the task of forming a caretaker government. The Greek constitution provides for such a move when there is no consensus.
Repeated attempts to form a coalition government have failed.
The new PM, the head of the Council of State Panayiotis Pikramenos, says he plans to include ministers from the last government and fellow judges in his cabinet.
The continued uncertainty has hit the euro and pushed stock markets down. The new elections could determine whether Greece remains a member of the eurozone.
The president has warned that fear over the state of Greek banks could turn into panic leading to an exit.
“Everybody is very worried, don’t you see what’s going on with bank liquidity? I hear that people are taking their money out of banks, they are worried that we might go back to the drachma, they are putting their money into safety deposit boxes, it’s crazy, it’s as if there is a war coming,” said economist Kleoniki Terzou.
The head of the European Commission José Manuel Barroso has warned that Greece’s bailout conditions cannot be modified.
The issue divided the country at the last election which saw no party gain a majority in parliament amid significant gains for anti-austerity parties.