The budget has already been given the green light by the lower house but the senate needs to give its nod as well, with the debate kicking off at 9:30 am (0830 GMT) and a vote expected to begin around 1:30 pm (1230 GMT).
Italy's President Sergio Mattarella called on Renzi, 41, to postpone his exit following his crushing referendum defeat until the budget is passed, in a bid to reassure those in Europe worried about the country's plunge into political uncertainty.
Renzi is expected to meet Wednesday afternoon with the top rung of his centre-left Democratic Party (PD) to discuss what decisions need to be taken in the short and medium terms — such as whether he will remain party head.
The former mayor of Florence will also likely meet with Mattarella at the presidential palace after the budget passes to officially resign.
Consultations between Mattarella and the political parties over choosing a caretaker prime minister and government could begin as early as Thursday and continue into Friday.