The three chosen from Africa are Stephen Brislin, 66, archbishop of Cape Town, South Africa; Protase Rugambwa, 63, co-adjutor archbishop of Tabora, Tanzania; and Stephen Mulla, 59, archbishop of Juba, South Sudan, which the pope visited earlier this year.
Pope Francis said he would appoint the new cardinals from across the world at the end of September at the assembly of cardinals known as a consistory.
It will be the ninth consistory called by the pope since his election 10 years ago as the first pontiff from Latin America.
"Their provenance expresses the universality of the Church that continues to proclaim God's merciful love to all people on earth," said the pope, following his weekly Sunday Angelus prayer from the window of the Apostolic Palace on Saint Peter's Square.
All cardinals under the age of 80, including 18 out of the group named on Sunday, are known as "cardinal electors," who will participate in the vote to nominate the successor to Pope Francis.
Following the consistory in September, there will be 137 cardinal electors, about three-quarters of whom will have been appointed by Francis.
Cardinals rank second only to the pope in the Church hierarchy and serve as his closest advisers. Due to their historical power and influence, they are still called the princes of the Church, although Francis has told them not to live like royalty and to be close to the poor.
Three of the new cardinals were recently named as heads of major Vatican departments, including Argentine Archbishop Victor Manuel Fernandez, head of the Vatican's doctrinal department.
Another significant appointment was that of Bishop Stephen Chow Sau-Yan of Hong Kong. Chow is one of the major links to the Catholic Church in communist China, where the Vatican is trying to improve conditions for Catholics. The bishop visited Beijing in April.
Another is Archbishop Robert Francis Prevost, an American who was recently named head of the Vatican department that helps the pope choose new bishops, one of the most powerful posts in the Vatican.
The other new cardinals come from countries including Italy, Switzerland, Spain, Colombia, Poland, Malaysia, and Portugal.
Information for this report came from Reuters, Agence France-Presse and The Associated Press.