Acosta is a Spanish and Portuguese surname. Originally it was used to refer to a person who lived by the seashore or was from the mountains (encostas). It comes from the Portuguese da Costa (cognate of English "coast"), which in Spanish became de Acosta. Notable people with the surname include:
- Agustín Acosta, Cuban baseball player
- Alberto Acosta (born 1966), Argentine footballer
- Alberto Martín Acosta Martinez (born 1977), Uruguayan footballer
- Rene Alexander Acosta (born 1969), American attorney and United States Secretary of Labor 2017–2019
- Alda Ribiero Acosta (contemporary), American terrorist in Uruguay
- Allan Acosta, American engineer
- Armando Acosta (contemporary), doom metal drummer, former member of the band Saint Vitus
- Bertrand Blanchard Acosta (1895–1954), American aviator who flew in the Spanish Civil War
- Carlos Acosta (contemporary), Cuban ballet dancer
- Cecilio Acosta (1818–1881), Venezuelan writer
- Cristóbal Acosta (1515–1580), Portuguese physician and natural historian
- Ed Acosta (born 1944), Panamanian Major League Baseball pitcher
- Eliades Acosta (born 1959), Cuban politician
- Jim Acosta (born 1971), CNN senior White House correspondent
- Joaquín Acosta (1800s), Colombian explorer and author
- Joe Acosta (born 1950), Puerto Rican salsa piano player
- José de Acosta (1540–1600), Spanish Jesuit missionary and historian to Latin America
- José Julián Acosta (1825–1891), Puerto Rican journalist and abolitionist
- Josephine Acosta Pasricha (1945–), Filipino Indologist and translator
- Juan F. Acosta (1890–1968), Puerto Rican composer and music teacher
- Julio Acosta García (1872–1954), President of Costa Rica 1920–1924
- Lautaro Acosta (born 1988), Argentine footballer
- Leopoldo Acosta (born 1962), Ecuadorian track and field athlete
- Luciano Acosta (born 1994), Argentine footballer
- Manuel Gregorio Acosta (1921–1989), Mexican-American painter
- Manuel da Costa (1541–1604), Portuguese Jesuit priest, teacher, and missionary
- Manny Acosta (born 1981) Panamian baseball player
- Marta Acosta, American fiction writer
- Martha Acosta (contemporary), Peruvian politician and congresswoman
- Mercedes de Acosta (1893–1968), Spanish-American poet, playwright, and designer
- Nelson Acosta (1944–), Uruguayan football player and coach
- Óscar Acosta (1933–), Honduran writer, critic, politician and diplomat
- Oscar Zeta Acosta (1935–1974), American attorney, author, politician, and activist
- Pablo Acosta Villarreal, Mexican drug lord
- Pedro Acosta (born 1959), Venezuelan football (soccer) defender
- Raúl Acosta (born 1962), Colombian road cyclist
- Rodolfo Acosta (1920–1974), Mexican character actor
- Santiago Acosta (born 1979), Argentine flyweight boxer
- Santos Acosta (1828–1901), President of Colombia 1867–1868
- St. Elmo W. Acosta (1900s), American politician from Jacksonville, Florida
- Teolindo Acosta (1937–2004), Venezuelan professional baseball player
- Tomás Diez Acosta (born 1946), Cuban revolutionary, teacher, and author
- Uriel da Costa (1585–1640), Portuguese philosopher and skeptic
Other
- Acosta (crater), lunar crater named after Cristóbal Acosta
- Acosta Bridge, bridge in Jacksonville, Florida named after St. Elmo W. Acosta
- Acosta (canton)
- Acosta Inc., Sales & Marketing company in Jacksonville, Florida
- Acosta (manufacturer), German catering equipment and coffee machine factory