Francis made a well-publicized visit to the island, home to migrants and refugees who have fled war and violence in the Middle East and North Africa. The Pope invited three Syrian migrant families to go with him as he returned home, the Holy See Press Office said.
The Vatican will take responsibility for the three families, the statement said. All are from Syria.
"The Pope has desired to make a gesture of welcome regarding refugees, accompanying on his plane to Rome three families of refugees from Syria, 12 people in all, including six children," the statement said.
These are people who were already in camps in Lesbos before a European Union-Turkey agreement
in which anyone crossing into Greece illegally from Turkey will be returned. All three families are Muslim. Two families come from Damascus, and one from Deir Ezzor, the statement continued. "Their homes had been bombed."
The families were selected in a lottery-type process, said Kathleen Prior, a spokeswoman for the humanitarian organization International Rescue Committee.
"The Pope has sent a strong message in relocating 12 people, including women and children, from three Syrian families from the camps on Lesbos," Prior said. "These refugees were randomly selected and are the very few lucky ones."
Little is known of the Pope's plans for the families. The initial hospitality will be taken care of by the Community of Sant'Egidio.
According to its website, the Community of Sant'Egidio
began in Rome in 1968, in the period following the Second Vatican Council.
"Today it is a movement of lay people and has more than 60,000 members, dedicated to evangelization and charity, in Rome, Italy and in more than 73 countries throughout the world," the website says.
In an interview with journalists on the plane after leaving Greece, the Pope said all nations have the responsibility of welcoming refugees.
"I have always said that building walls is not a solution," he said. "We saw walls during the last century and they did not resolve anything. We must build bridges. Bridges are built with intelligence, with dialogue, with integration."
U.N. High Commissioner for Refugees Filippo Grandi praised the pope's gesture, calling it "a powerful demonstration of solidarity. It must inspire governments and societies in a world where the desperate plight of record numbers of forcibly displaced is too often met by barriers, rejection and fear."
Refugees on Lesbos deeply moved
Lesbos houses thousands who have fled Syria, Iraq, Afghanistan and other countries plagued by war and poverty in the last year. Thousands have drowned or gone missing after trying to cross the Mediterranean to peripheral European land such as Lesbos.
Francis visited the island with the leader of the Orthodox Christians, Ecumenical Patriarch Bartholomew, and Archbishop Ieronymos II of Athens.
From its beginning, the visit was deeply moving to the refugees.
Some broke down in tears, with one man shaking as he asked, "Father, bless me. Please, bless me."
Children took pictures of the Pope with their phones as he shook hands with those gathered to greet him.
At the port, Francis offered a prayer to God for "all the men, women and children who have died after leaving their homelands in search of a better life."
"Though many of their graves bear no name, to you each one is known, loved and cherished," the Pope said.
In the 24 hours before the Pope's arrival, 125 migrants and refugees streamed into the Greek islands from Turkey, according to Greek government figures.
Pope: 'I embrace all in affection'
The Pope comforted the refugees he met, sharing a message on empathy.
"I have wanted to be here with you today to speak with you and tell you: You are not alone. You have endured much suffering in your search for a better life," the Pope said. "You have made great sacrifices for your families."
"May the world, the Good Samaritan, come to your aid with respect for human dignity," he said.
In explaining his prayers for the refugees and migrants, Francis invoked the name of the Lord.
"I embrace all in affection," he said. "I invoke his gift of strength and peace."