Dalbono's father was the literary scholar and art critic Carlo Tito Dalbono. Around 1850 Eduardo was taught by the engraver Augusto Marchetti in Rome. He then enrolled at the Accademia in Naples, where his teachers were Giuseppe Mancinelli and Domenico Morelli. Dalbono also studied with Nicola Palizzi. His interests were divided between historical themes, landscapes and folklore subjects.
From 1872 he settled in Paris for about four years, where he met the art dealer Goupil thanks to his friend de Nittis. He worked for him, executing Neapolitan motifs of great charm.
From 1897 he had a chair of painting at the Royal Institute of Fine Arts and in 1905 he became curator of the Pinacoteca of the National Museum of Naples.