The International Olympic Committee made the announcement Friday after whittling down the shortlist from 43 athletes, while it also confirmed that 15 officials will accompany the team.
Competing under the Olympic flag, the six male and four female athletes will walk into the opening ceremony at the Maracana Stadium ahead of host country Brazil.
Rami Anis, a Syrian swimmer living in Belgium, was the first name announced. He was joined by South Sudan 800-meter runner Yiech Pur Biel and compatriots James Nyang Chiengijek, a 400m specialist, and Paulo Amotun Lokoro, a 1,500m runner.
Yomas Kinde, from Ethiopia, will compete in the marathon, while Popole Misenga, from the Democratic Republic of Congo, will take part in the 90 kg judo category.
Two of the four women included are from South Sudan, with Anjelina Nada Lohalith selected to compete in the 1,500m and Rose Nathinke Lokonyen in the 800m.
Yolande Bukasa Mabika, who left the Democratic Republic of Congo before seeking asylum in Brazil in 2013, will be involved in the 70 kg judo while 18-year-old Yusra Mardini
, who left Syria before settling in Germany, will be hoping to make a splash in the swimming pool.
"These refugees have no home, no team, no flag, no national anthem," IOC president Thomas Bach said.
"We will offer them a home in the Olympic Village together with all the athletes of the world. The Olympic anthem will be played in their honor and the Olympic flag will lead them into the stadium.
"This will be a symbol of hope for all the refugees in our world, and will make the world better aware of the magnitude of this crisis," Bach added.
"It is also a signal to the international community that refugees are our fellow human beings and are an enrichment to society.
"These refugee athletes will show the world that despite the unimaginable tragedies that they have faced, anyone can contribute to society through their talent, skills and strength of the human spirit."
The United Nations' refugee agency said it was "very inspired" by the creation of the historic team. It said the global number of refugees, asylum seekers and displaced peoples had continually risen since the 59.5 million recorded at the end of 2014.
"Having had their sporting careers interrupted, these high-level refugee athletes will finally have the chance to pursue their dreams," UN High Commissioner for Refugees Filippo Grandi said in a statement.
"Their participation in the Olympics is a tribute to the courage and perseverance of all refugees in overcoming adversity and building a better future for themselves and their families."