ROME—A party revolt forced Italian Prime Minister Enrico Letta to resign, clearing the way for the ascent of a rival who has promised to shake up Italy's sclerotic political system and try to reverse an alarming decline of the euro zone's third-largest economy.

Mr. Letta's departure will bring to an end a 10-month-old government that has teetered since its formation last spring and has come under fire for failing to combat Italy's worst economic crisis since World War II. His probable successor is party rival Matteo Renzi,...