Almeida was born on 15 March 1957 in São Sebastião da Pedreira, Lisbon, Portugal, the son of João Baptista de Almeida and Maria Sara Portugal. At the age of eighteen, after attending a theater course at the Lisbon Conservatory (School of Theatre and Cinema) for two years, he left Portugal to continue his studies after the Conservatory was temporarily closed following the 1974 democratic revolution. He spent a year in Vienna, moving again, in 1976, to New York City where he studied at the Lee Strasberg Theatre and Film Institute, a school for the performing arts.