NABA is a private Academy that was founded in Milan in 1980 on the initiatives of Ausonio Zappa, Guido Ballo and Tito Varisco who aimed at challenging the rigid academic tradition by introducing new visions and languages closed to contemporary artistic practice and the creative and artistic professions. In 1981 it was officially recognised by the Ministry of Public Education (now known as The Ministry of Education, University and Research).

A group of renowned artists with a strong vocation for teaching, among whom Kengiro Azuma, Emilio Isgrò, Carlo Mo, Emilio Tadini, Gianni Colombo, Lucio Del Pezzo, Franco Grignani, Mario Carieri, Umberto Mariani, Roberto Menghi, Aldo Montù, Waler Valentini, Gino Negrii, Hidetoshi Nagasawa started to collaborate with the Academy. Gianni Colombo, artist, designer and Director of the Academy from 1985 to 1993, shaped the NABA educational philosophy. In 1984 the Advertising and Graphic Design Curriculum was added to the Painting, Sculpture and Theatre Design Programs and in 1988 Fashion Design Program was added to the NABA programs. An internationalisation process was meanwhile launched and in 1990 NABA joined ELIA (European League of Institutes of the Arts).

In 1995 NABA was awarded by The Mayor of Milan the Certificate of Civic Merit with the following motivation: ”NABA has grown in prestige and fame and has become the Italian reference point for Fine Arts Academies in Europe and worldwide.”

In 1997, a Bachelor of Arts Degree Program in Product Design was activated. In 2002, NABA joined the Bastogi Group and integrated Futurarium, a post-graduate School of aesth-et(h)ics founded by Alessandro Guerriero, who is currently NABA President. NABA current Director is Elisabetta Galasso. Between 2003 and 2004 NABA moved to the new prestigious campus in via Darwin 20, Milan.

In the Academic Year 2006/2007 the first two-year MA Programs and one-year Master Programs were activated: the two-year MA Program in Visual Arts and Curatorial Studies, the one-year Master Programs in Digital Environment Design, the one-year Master Programs in Photography and Visual Design (in collaboration with FORMA - International Centre for Photography), as well as the one-year Master Program in Landscape Design, in collaboration with Politecnico di Milano.

In January 2008 NABA activated the one-year Master Program in Interior Design, as well as the two-year MA Programs in Multimedia Communication Design and in Textiles and new Materials Design. In the Academic Year 2010-2011, a new  two-year MA Program in Film and New Media was activated.

Starting from the Academic Year 2010-2011 another two-year MA Program in Design will be activated.

Since 2005 the academy has also been part of the PhD Program in Arts and Technologies developed by the Planetary Collegium based at Plymouth University (UK).

On 21st December 2009 NABA joined Laureate Education, an international network of accredited universities that includes a community of over 650,000 students on more than 100 campuses in North America, Latin America, Europe and Asia.