In 1886, he received an honorable mention for his works in the Salon des Artistes Français, where he exhibited regularly until 1913.
It is thought he moved to Mexico City in 1889, where he quickly won critical acclaim for his marble and bronze busts of Mexican personalities.
In 1891 he was commissioned by the Mexican government to create statues of national heroes for Paseo de la Reforma, in Mexico City.
Alciati was appointed professor of sculpture, decoration and modelling at the Escuela Nacional de Bellas Artes in 1895.
At the beginning of the 20th century he was commissioned by the then President Porfirio Díaz to create most of the sculptures for the Independence Column in Mexico City under the direction of Antonio Rivas Mercado.