Francis has sent the letter, written in Spanish, to members of the team who are competing in the four-yearly global competition.
The refugee team is the first of its kind to be created for the Olympics and includes ten members from countries including South Sudan, Syria and the Democratic Republic of the Congo.
Who's in the refugee team:
1. Rami Anis, a swimmer from Syria
2. Yiech Pur Biel, a sprinter from South Sudan
3. James Nyang Chiengjiek, a sprinter from South Sudan
4. Yonas Kinde, a runner from Ethipia
5. Anjelina Nadai Lohalith, a runner from South Sudan
6. Rose Nathike Lokonyen, a sprinter from South Sudan
7. Paulo Amotun Lokoro, a runner from South Sudan
8. Yusra Mardini, a swimmer from Syria
9. Popole Misenga, a judoka from the Democratic Republic of the Congo
10. Yolande Bukasa Mabika, a judoka from the Democratic Republic of the Congo
One of the team, Yusra Mardini, is a well-known Christian refugee after she swam for three hours in the sea to reach safety.
The 19-year-old and her sister then helped to save the lives of 20 refugees by dragging their boat to safety in open water when the motor broke down.
She will compete in the women's 100m freestyle heats on Wednesday.
Vatican Radio translated the letter Pope Francis wrote: "I extend my greetings and wish you success at the Olympic Games in Rio - that your courage and strength find expression through the Olympic Games and serve as a cry for peace and solidarity."
He went on: "Humanity would understand that peace is possible, that with peace everything can gained, but with war all can be lost.
"Your experience serves as testimony and benefits us all."
Yusra Mardini is the first to compete for #RefugeeOlympicTeam in Women's 100m Butterfly today at 13:28 Rio time. https://t.co/gRcmwyh32F
— Refugee Olympic Team (@RefugeesOlympic) August 6, 2016
