Chapí was born in the small Spanish village of Villena, near Alicante. His father, a barber, was an amateur musician who gave his son his first music lessons. By the time young Ruperto was 9, he was not only an accomplished cornet player, but he had started to arrange music for bands and even composed his own works. At 14 he was conducting a local band; his rare musical gifts allowed him to enter the Madrid Conservatory at the age of 16. There, under the guidance of Emilio Arrieta (composition) and Miguel Galiana (harmony), he won first prize in harmony in a competition in 1869.
To support himself in his student years he played cornet in the Circo de Price theater orchestra. During this period he composed his first surviving zarzuela, Abel y Caín, which was premiered in 1873. An opera, on a commission arranged in part by Arrieta, followed quickly, Las naves de Cortés (1874). Its success brought Chapí government funding for three years of study abroad (Rome, Milan, Paris), and also prompted him to abandon his post of conductor of a military band, which he had held since 1871.
From 1874 until the end of his career, Chapí focused almost exclusively on composition. He wrote several operas while studying abroad, then returned to Madrid in 1878. His second zarzuela, Música clásica, premiered in 1880 and was followed by a steady string of zarzuelas over the next three decades. They generally achieved success, with a fair number receiving 100 or more performances. In 1889 Chapí, increasingly aware of artists' lack of rights in regard to copyright issues, rebuffed an offer to join the Academia de Bellas Artes because of its insensitivity to artists' rights. Ten years later he founded the Society of Authors to champion the issue in Spain. In 1905, Chapí's four string quartets appeared, signaling his suddenly more serious approach to composition. In 1909 Chapí became ill while leading a performance of his final opera, Margarita la tornera, and died a short while later.