He began to study Latin and Philosophy in Monforte, finishing them and taking his degree in Law in Valladolid. In 1821, he was nominated magistrate in Seville, filling this office until 1823. Afterwards, he returned to Valladolid.
Manuel de Acosta was the author of the manuscript titled Papeles varios que el licenciado don Manuel de Acosta, relator de la Chancillería de Valladolid, ha copiado o hecho copiar de diferentes libros, para uso o instrucción en la Historia nacional, eclesiástica y civil.