Rapetti attended the School of Decorative and Figural Art at the Brera Academy in Milan , under the guidance of Raffaele Casnedi and Giuseppe Bertini. After the death of Tranquillo Cremona (1878) he joined the artists affiliated with the Grubicy Gallery, founded in 1876 by the brothers Vittore and Alberto and for which he specialized in the creation of watercolours intended for the French market, often reproducing the subjects of Cremona's paintings. Rapetti participated in the annual Brera exhibitions, winning, in 1880, the Fumagalli Prize with a portrait commissioned by Vittore Grubicy. In 1882 he won a prize that allowed him to spend a period of study and improvement in Rome and later visited Paris and London. Back in Milan, he opened a studio in Corso Venezia 46 where he taught painting privately. From 1887, the year in which he moved his studio to via Rossini 3, he worked for over forty years as a figure drawing teacher at the Brera Academy, at the same time dedicating himself to commissioned portraits, both from private individuals and from public institutions in Milan. Rapetti also received several commissions as a decorator and fresco painter of civil buildings in Milan, and several religious monuments such as the Church of the Ospedale Maggiore. He participated in the Turin Quadrennial of 1902, the National Exhibition of Fine Arts in Milan in 1906 and the First Exhibition of Milanese Artists organized by the Famiglia Meneghina.