He graduated in mathematics at the University of Pavia, where he was a pupil of Antonio Bordoni. For a long period Codazzi taught first at the Ginnasio Liceale of Lodi, then at the liceo of Pavia. Meanwhile, he devoted himself to research in differential geometry.
In 1865, he was appointed professor of complementary algebra and analytic geometry at University of Pavia. He remained in his position at Pavia until his death in 1873.
- E. Beltrami sulle "Memorie per la storia dell'Università di Pavia", serie 13 (1878).
- U. Amaldi, in Enciclopedia italiana, app. 1, Rome, (1938), 438.