It is thought he will take the role in a ceremonial capacity while he finishes his studies at Oxford University.
Bilawal told journalists at the Bhutto family home: "My mother always said democracy is the best revenge."
Ms Bhutto's widower, Asif Ali Zardari, who is expected to run the party, said it would contest January elections.
And he appealed to the former prime minister Nawaz Sharif to drop his threat to boycott the polls.
"Today's general would like to run (from the election)," he said, in a reference to President Musharraf. "We would not like to give him that chance."
Mr Zardari and his son were speaking at a news conference after a meeting of the leadership of the PPP to hear Ms Bhutto's political will.