Céspedes was born in the small town of Campechuela, in Granma Province, Cuba. Céspedes is the son of Estela Milanés, a softball pitcher who appeared in the 2000 Summer Olympics for Cuba, and Cresencio Céspedes, a former Cuban League catcher who separated from Milanés when Yoenis was one year old. At age 10, he was sent by his mother to a state-run school where he could focus on baseball. He played eight seasons in the Cuban Winter League before defecting from Cuba in 2011. In the summer of 2011, Céspedes and six others took a 23-hour speedboat ride departing Cuba and heading for the Dominican Republic. After arriving in the Dominican, he met Dominican agent Edgar Mercedes who established residency for him in Santiago which allowed him to bypass the MLB Draft and become a free-agent.