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.
No known precedent
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.
In 1294, former hermit Celestine V resigned after five months as pope. Boniface VIII was elected days later, and had his predecessor imprisoned. Celestine was dead within a year.
In contrast, Pope Francis has spoken warmly of his predecessor.
One of his first acts as Pope was to call Benedict at Castel Gandolfo, where the former pontiff had been following proceedings on television.
The pope emeritus is expected to stay on at the papal summer residence until new accommodation being prepared for him inside the walls of Vatican City is ready at the end of April.
For his part, Pope Francis will begin the Church’s most important liturgical season on Sunday with a Palm Sunday Mass in St Peter’s Square.
He will then lead six more liturgies during the week, culminating with the Easter Sunday Mass and Urbi et Orbi blessing.
The new Pope chose the name Francis in honour of St Francis of Assisi – the 13th Century Italian saint who spurned a life of luxury to work with the poor.
He has called for the Roman Catholic Church to be closer to ordinary people, especially the poor and disadvantaged.
And, only 10 days into his pontificate, he has made some subtle but significant changes in the lifestyle of the leader of the Roman Catholic Church, says our correspondent.
He dresses very simply, preferring to wear plain black shoes under a simple white habit rather than the red leather loafers and ermine-trimmed cape worn by his predecessor.
The first Latin American Pope spurned a special car to take a bus with his cardinals after he was elected, and insisted on returning to his Rome hotel the next day to pay his own bill.
And Pope Francis places himself on the same level as his guests, rather than greeting them from a throne on an elevated platform, which is seen as a powerful gesture after centuries of Vatican pomp.
The former archbishop of Buenos Aires has also started inviting guests to his early morning Mass – including Vatican gardeners, street sweepers, kitchen staff and maids working at the hotel where he is currently staying.
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