Party leader Matteo Renzi had earlier called for a change of government at a party meeting, saying the country could not go on in “uncertainty”.
Speculation has been rife that Matteo Renzi wants to take over as prime minister.
Matteo Renzi is eight years younger than Enrico Letta and was elected leader of the party in December.
Enrico Letta said in a statement that his decision followed “the decision taken today by the national leadership of the Democratic Party”.
He said he would formally submit his resignation to President Giorgio Napolitano at the presidential palace on Friday.
Matteo Renzi has previously accused Enrico Letta of a lack of action on improving the economy, with unemployment at its highest level in 40 years and the economy shrinking by 9% in seven years.
Correspondents say that although the prime minister has kept a careful lid on public expenditure, he has not been able to carry out much-needed administrative reforms and stimulate economic growth.
The latest political turmoil has so far had little impact on financial markets, in contrast with the volatility seen before the current coalition was formed.
Enrico Letta did not attend Thursday’s party meeting, which had been brought forward from next week.
At the meeting, Matteo Renzi thanked Enrico Letta for his “remarkable work” but said the country could not go on in “uncertainty”.
He said his proposal – a new government to take over until the end of the current parliamentary term in 2018 – was a way out of the “morass”.
Enrico Letta, 47, formed a coalition with the centre-right last year but there had been mounting speculation over his future after Matteo Renzi was elected party leader in December.
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