Napolitano said there was not sufficient support for a broad coalition government, as demanded by Silvio Berlusconi, who was prime minister before Prodi, and other conservatives.
The president, who consulted all Italian parties in the parliament, said most party leaders agreed that early elections without a change in Italy's electoral law - which has increased the influence of small parties - was pointless.
"It seemed clear that there was no concrete alternative," he said.
"Looking at Italy's delicate European and international commitments and the pressing need for economic and social reform, we must express our concern and hope that the country can be governed in a credible and stable fashion," he said.
Italian media reported that the vote of confidence would take place on Wednesday or Thursday.
Prior to Napolitano's announcement, Prodi appeared to have succeeded in gaining at least one extra senator to bolster his weak majority in the upper house.
Prodi's nine-party coalition currently has only a single-seat advantage.
Marco Follini, a Christian Democrat who briefly served as deputy prime minister in Silvio Berlusconi's government, said he would "probably" support Prodi in a confidence vote.
Prodi should also be able to count on the support of a majority of the seven senators-for-life, non-elected elder statesmen.
Gianfranco Fini, head of the opposition National Alliance, said it would be a "democratic anomaly" for Prodi to return to power without a guaranteed majority in parliament.
"The head of state must ensure that in the senate there is a political majority even without the votes of the life senators," he told Corriere della Sera daily.
The possibility of snap elections that might return Berlusconi to power after just nine months in opposition appears to be the main catalyst for the centre-left's newfound cohesion.