Italy's previous election was held two years ago.
Origin of crisis
Prodi's 20-month-old centre-left government fell last month after a small centrist party within the ruling coalition pulled out.
After that, attempts were made to form an interim government, which would have been entrusted with making changes to the voting system.
Napolitano had asked Franco Marini, the senate speaker, to try to engineer an interim government that could oversee amendments to Italy's electoral law, but the effort failed.
Silvio Berlusconi, Italy's conservative former prime minister, has consistently rejected any possibility of an interim government.
Walter Veltroni, leader of Prodi's coalition, had hoped to delay the election by supporting the idea of an interim government and mooted changes to the electoral law.
The proportional representation vote system was passed in the last months of Berlusconi's 2001-06 term but was widely criticised.
It is widely seen as giving too much power to small parties, thus increasing the risk of political instability should such groups leave the government.
Berlusconi, 71, whose centre-right coalition is leading in the opinion polls, is well placed to return to power.