Pope Francis was flown by helicopter to Castel Gandolfo for the private lunch with Pope Emeritus Benedict.
Benedict has lived at the lakeside castle south of Rome since last month, when he became the first pope in six centuries to resign, citing ill health.
Cardinal Jorge Maria Bergoglio was elected to succeed him on 13 March.
There was no official communique on the results of the Pope’s brief lunchtime visit to Castel Gandolfo, says the BBC’s David Willey in Rome.
On the agenda, some delicate handover details, including a top secret document prepared by the former pope on last year’s scandal involving leaked documents, our correspondent adds.
The new head of the Catholic Church is usually elected after the death of his predecessor, and there is no public record of any previous meeting between an incumbent pope and a former pope.