Acosta was born in Havana, Cuba, in 1958. He attended the San Alejandro Academy, and later on the Superior Institute of Art (ISA), both in Havana. Acosta left Cuba in 1993 and moved to Miami in 1994.
Over the years Acosta has produced an extensive body of work and has presented many personal exhibitions. Among these should be mentioned a touring one in Brazil, which began at the Caixa Cultural de Rio de Janeiro and ended at the Caixa Cultural in Sao Paulo. His work has been included in several collective exhibitions; and can be found in museums and institutions such as the National Museum of Fine Arts, Havana, Cuba; Wifredo Lam Center, Havana, Cuba; Museum of Contemporary Art, MOCA. Miami, Florida; Lowe Art Museum, Miami, Florida; Fort Lauderdale Art Museum, Fort Lauderdale, Florida; Nassau County Museum of Art, New York; and the Museum of Contemporary Art, Panama.
Since the beginnings of his career he has been interested in architecture as a symbol of power. His urban renderings place him, at times, as an observer, and others as a commentator on the social and political aspects that architecture represents. Acosta’s work speaks to the dialectical processes of life – birth and death – through urban vignettes of cities. Over the years he has been portraying the different places where he has lived, sometimes while living there and then again after having moved away.