He was born in Ozumba in 1737, the child of Felipe de Alzate and María Josefa Ramírez, a descendant of Juana Inés de la Cruz. He studied in the Colegio de San Ildefonso in Mexico City, graduating as a bachelor in theology in 1756. A priest from the age of 20, he was also a corresponding member of the French and Spanish academies of science, and one of the earliest trustworthy observers of Mexican meteorology. He attained a high reputation as a zoologist and botanist, and his researches led the way for modern exploration of Mexican antiquities. He published the Gaceta de Literatura, and an essay titled La limite des niéges perpetuelles en Volcan Popocatepetl.
The natural sciences, physics, astronomy and mathematics were for him subjects that deserved great attention. He conducted several scientific experiments, and wrote numerous articles that were published in science journals.
Inaugurated in 1768, his Diario literario de Méjico [Literary Newspaper of Mexico] was suspended after only three months. He later created, in 1788, the Gaceta de Literatura [Newspaper of Literature], that was published until 1795 (115 issues). This periodical inspired many of his countrymen to follow his example. His account of Xochicalco was the first published description of these interesting ruins.
More than thirty treatises on various subjects are due to his pen. Among other works, he wrote Observaciones meteorológicas [Weather observations] (1769), Observación del paso de Venus por el disco del Sol [Observation of the passage of Venus by the disc of the Sun] (1770), Modelo y descripción de los hornos de Almadén [Model and description of the furnaces of Almadén], notes, additions and maps for the Historia Antigua de México [Ancient History of Mexico], written by Francisco Javier Clavijero, and a Mapa de la América del Norte [Map of North America].
Astronomy, physics, meteorology, antiquities, and metallurgy, were among the topics on which he wrote, but he also devoted serious attention to certain industries. Thus the growing of silk in Mexico was the subject of several of his papers. He wrote a dissertation on the use of ammonia in combating mephitic gases in abandoned mines, and also prepared maps of New Spain (Mexico). In 1772, he published work that showed that the well-known psychedelic effects of pipiltzintzintli were due to natural causes and not the work of the devil (Memoria del uso que hacen los indios de los pipiltzintzintlis; México, D.F.: Universidad Nacional Autónoma de México). He was frequently opposed, even reviled, at home, but the French Academy of Sciences made him a corresponding member, and the viceroys of Mexico and the archbishops entrusted him with sundry scientific missions.
In his honor, the Sociedad Científica Antonio Alzate [Antonio Alzate Scientific Society] was created in 1884. In 1935, this society became the National Academy of Sciences. A dam and reservoir are named in his honor in the State of Mexico, north of Toluca. Plant genus Alzatea is named after him