The three Muslim families are being housed temporarily by the Saint'Egidio religious community in the Rome district of Trastevere while they await longer-term accommodation being prepared for them in the Vatican, community spokesman Maximiliano Signifredi told AFP.
"Yesterday they had their first Italian lessons. They have been going for walks around Trastevere, a new life is opening up in front of them," Signifredi said.
"Each of the three families has been assigned a small flat with everything they need while they are awaiting the more spacious apartments the Vatican is getting ready for them."
In a dramatic gesture designed to highlight the plight of hundreds of thousands of refugees arriving on the southern shores of Europe, Francis on Sunday flew back from Lesbos with the 12 Syrians.
The three couples, who have six children between them, were plucked from a detention camp on the Greek island to start new lives, more than 1,400 miles (nearly 2,300 kilometres) from their homes in Damascus and Deir Ezzor, a city in eastern Syria controlled by the Islamic State group.
Francis said on the plane back from Lesbos that the families had been chosen out of some 3,000 people at the camp simply because their paperwork was sufficiently in order to rapidly conclude an accord on their transfer with the Greek and Italian governments.
"I didn't make a choice between Christians and Muslims. All refugees are children of God," Francis told reporters.
The families are expected to seek asylum in Italy rather than through the tiny Vatican city state.
One of the Syrians, a 51-year-old teacher from Deir Ezzor, has said the families, who had planned to try and get to Germany via Greece, do not know what awaits them.
"We don't know whether we will start over in Europe or whether, one day, we will be able to return to a Syria free of war and violence," the teacher, identified only as Ramy, told Italian media at the weekend.
The Vatican was already housing two Syrian families in line with Francis's instruction to every Catholic parish in Europe to take in at least one.
The St Egidio community is very active on migration issues and has organized flights to Rome for dozens of Syrian refugees who are housed in the same building as the families brought back by the Pope.