FTSE Milano Italia Borsa closed at 20,436 points, up 1.62 percent, posting one of the strongest gains among European exchanges during Friday trading, the Italian news agency ANSA reported.
The spread between Italy's 10-year bond and its German counterpart narrowed slightly during the day, closing at 200 basis points after ending the previous trading session at 204 basis points.
The yield on Italy's 10-year bond dipped slightly to 3.68 percent, down from 3.70 percent Thursday.
Letta's departure cleared the way for the likely appointment of Democratic Party colleague Matteo Renzi to take on the position.
If the 39-year-old Renzi, the mayor of Florence, is named prime minister, he will be the youngest premier in Italy's history and the country's third consecutive non-elected prime minister in two years.