The ceremony to install them, known as a consistory, will be held on September 30, the 86-year-old Francis announced on Sunday during his noon prayer to pilgrims and tourists in St Peter's Square.
Eighteen of the churchmen are younger than 80 and will be able to enter an eventual conclave to choose the next pope.
The other three, who are older than 80 and too old to vote in a conclave, were named to thank them for their long service to the church.
All cardinals, regardless of their age, are allowed to take part in pre-conclave meetings known as general congregations, giving them a say in the type of person they think their younger brother cardinals should choose.
The new cardinals come from countries including the United States, Italy, Argentina, South Africa, Spain, Colombia, South Sudan, Hong Kong, Poland, Malaysia, Tanzania and Portugal.
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.
