Beltrami was born in Milan. He was initially a student at the Politecnico in Milan, then in the Brera Academy, where he studied under Camillo Boito. From there he moved to Paris, where he stayed till 1880. He was involved in works at Trocadero an at the Palace of the National Exhibitions. He was able to outscore those taking tests from the Ecole Nationale de Beaux Arts, and distinguished himself at the Salon with designs by aquaforte. He was nominated the second in command as inspector of the works of reconstruction at the Hotel de Ville of Paris. He collaborated with the architect Théodore Ballu in works on the Palace of Justice at Charleroi, Belgium.
Returning from Paris in 1880, he won a contest for the Cathedra of Geometry and Descriptive Architecture at the Academy of Fine Arts of Milan. By commission from the Ministry of Public Instruction, he recorded all the reliefs found at the Lazzaretto of Milan; the Castello Sforzesco of Milan, and the Rocca of Soncino. He was responsible for the restoration of the Castello Sforzesco. He won a contest to design the Facade of the church of San Sebastiano in Biella, and a prize for his second design (submitted from Paris) for the Monument delle Cinque Giornate of Milan; and a third place prize for his design of the Hospital General of Charity in Turin.
He is buried at the Cimitero Monumentale di Milano.
- 1896 : member of the Royal Academy of Science, Letters and Fine Arts of Belgium. 
- Dizionario degli Artisti Italiani Viventi: pittori, scultori, e Architetti., by Angelo de Gubernatis. Tipe dei Successori Le Monnier, 1889, page 49-50.
- An inscription on the pedestal incorrectly identifies Beltrami as the sculptor. The bronze statue was actually the work of Luigi Secchi: see Chi era Costui — Scheda di Giuseppe Parini
- Royal Academy of Science, Letters and Fine Arts of Belgium
Media related to Luca Beltrami at Wikimedia Commons
- Varagnoli, Claudio (2007–2008), "Conservazione e ripristino in Italia nel secondo Ottocento. Il rapporto storia-restauro in Luca Beltrami.", Corso di "Teoria e storia del restauro": Appunti dalle lezioni (PDF), Università degli Studi di Chieti e Pescara – Facoltà di Architettura. (Class notes for a course on the theory and history of architectural restoration.)