Catholics could be elected as soon as Palm Sunday, on March 24, and be ready to take over by Easter a week later, Lombardi said.
Several popes in the past, including Benedict's predecessor John Paul, have refrained from stepping down over their health, because of the division that could be caused by having an "ex-pope" and a reigning pope alive at the same time.
Lombardi said the pope did not fear a possible "schism", with Catholics owing allegiances to a past and present pope in case of differences on Church teachings.
He indicated the complex machinery of the process to elect a new pope would move quickly because the Vatican would not have to wait until after the elaborate funeral services for a pope.
It is not clear if Benedict will have a public life after he resigns. Lombardi said Benedict would first go to the papal summer residence south of Rome and then move into a cloistered convent inside the Vatican walls.
The resignation means that cardinals from around the world will begin arriving in Rome in March and after preliminary meetings, lock themselves in a secret conclave and elect the new pope from among themselves in votes in the Sistine Chapel.
There has been growing pressure on the Church for it to choose a pope from the developing world to better reflect where most Catholics live and where the Church is growing.
"It could be time for a black pope, or a yellow one, or a red one, or a Latin American," said Guatemala's Archbishop Oscar Julio Vian Morales.
The cardinals may also want a younger man. John Paul was 58 when he was elected in 1978. Benedict was 20 years older.
"We have had two intellectuals in a row, two academics, perhaps it is time for a diplomat," said Father Tom Reese, senior fellow at the Woodstock Theological Center at Georgetown University. "Rather than electing the smartest man in the room, they should elect the man who will listen to all the other smart people in the Church."
Liberals have already begun calling for a pope that would be more open to reform.
"The current system remains an 'old boy's club' and does not allow for women's voices to participate in the decision of the next leader of our Church," said the Women's Ordination Conference, a group that wants women to be able to be priests.
The last pope to resign willingly was Celestine V in 1294 after