Castiglioni was born on 16 February 1918 in Milan. He was the third son of the sculptor Giannino Castiglioni and his wife Livia Bolla. His older brothers Livio and Pier Giacomo were both architects and product designers. Achille Castiglioni paired with his brother Pier Giacomo planned serial production objects for companies such as Kartell, Zanotta, Flos, Bernini, Siemens, Knoll, Poggi, Lancia, Ideal Standard, Arflex, and Alessi.

In 1937 he enrolled in the faculty of architecture of the Politecnico di Milano and graduated in March 1944. When the War was over, Castiglioni joined the architectural design practice that his brothers Livio and Pier Giacomo had started with Luigi Caccia Dominioni in 1938. Much of their work was in exhibition design, but they also carried out a number of architectural projects, including the reconstruction in 1952-53 of the Palazzo della Permanente, which had been destroyed by bombing in 1943.

On 1952, Livio Castiglioni left the practice and A. Castiglioni run the office with his brother Pier Giacomo. On 1968, Pier Giacomo passed away and A. Castiglioni worked alone. From 1969 he taught architectural and design subjects, first at the Politecnico di Torino, and then, from 1980 when he became professor, at the Politecnico di Milano.