The king chose
Charles III held a competition, with designs by Spanish architects like Ventura Rodríguez, but chose the Italian Francesco Sabatini's project himself.
Finished in 1778, the Puerta de Alcalá was one of the royal gates into Madrid, built by Charles III for travellers arriving from Alcalá de Henares, Aragon and France. The city later grew around it.

Charles III held a competition, with designs by Spanish architects like Ventura Rodríguez, but chose the Italian Francesco Sabatini's project himself.
The two sides of the gate are not the same: the decoration on the side facing the old road out of the city differs from the side facing the centre.
The inscription reads REGE CAROLO III ANNO MDCCLXXVIII: in the reign of Charles III, in the year 1778.
King Charles III commissioned it; the Italian architect Francesco Sabatini designed it, and it was finished in 1778.
It was the gate on the road to Alcalá de Henares, the route from Aragon and France.
Yes. It was finished in 1778, decades before the Arc de Triomphe in Paris (1836).