Mr Fischer takes over in the middle of the Czech Republic's EU presidency
Czech President Vaclav Klaus has appointed a new prime minister, drawing a line under the crisis caused by last month's resignation of Mirek Topolanek.
Jan Fischer, the former head of the Czech Statistical Office, will formally take over next month and lead the country until elections due in October.
Mr Topolanek stepped down after losing a confidence vote two weeks ago.
Mr Fischer's government will be backed by Mr Topolanek's Civic Democrats and the opposition Social Democrats.
The BBC's Rob Cameron in Prague says almost no-one in the Czech Republic has heard of Mr Fischer, but that is about to change.
Mr Fischer, a 58-year-old economist, will act in a caretaker role to take the country to early elections, probably in October.
For the next four weeks, Mr Fischer will be charged with putting together a non-partisan cabinet of technocrats, who will be appointed on 9 May.
But, our correspondent says, that will be no easy task as the names will be vetted by the two main parties.
In fact, he adds, thanks to a quirk of its rather vague constitution, the Czech Republic now has two prime ministers - Mr Topolanek, who continues to run the country in an acting capacity, and Mr Fischer, who will replace him in a month.
Our correspondent says a big question, however, is not who is in charge of the country, but who is in charge of the European Union.
Mr Topolanek was ousted by parliament halfway through the Czech Republic's six-month presidency of the EU and the country must still preside over a number of important summits.
They include a meeting in June on how to complete ratification of the Lisbon Treaty, which aims to reform how the EU is run.
President Klaus, who opposes the treaty, has assured the EU that the presidency will be completed successfully, and has offered personally to intervene.