Steele will leave his post at the AA next year, after serving as academic leader and chief executive of the institution since 2005.
As dean of the UCLA School of the Arts and Architecture, he will oversee its programmes encompassing art; architecture and urban design; design and media arts; and world arts and cultures and dance.
Steele will also take charge of the school's Fowler Museum and Hammer Museum, as well as the Center for the Art of Performance at UCLA.
His leadership will commence in August 2017 when he takes over from David Roussève, who has served as interim dean since July 2015.
"I am honoured and excited to be appointed dean and to join the UCLA School of the Arts and Architecture," said Steele.
"I look forward to working with everyone across all four of the brilliant departments in the school and with the inspiring directors and their teams at each of the incredible public arts units."
During his 11 years as director of the AA – the seventh ranking school in the Dezeen Hot List – Steele launched the AA Visiting School in Dubai, and a worldwide network of short courses and design research workshops.
He also initiated the AA Interprofessional Studio – an MA/MFA programme that explores alternative forms of interdisciplinary collaboration through the research, conception, design and production of genre-defying construction and spatial performance.
Steele was born in the USA, and grew up in Oregon and Idaho, before moving to the UK and eventually becoming a naturalised British citizen.
He first began working at the AA in 1996, when he co-founded the AA Design Research Lab – the institution's first-ever full-time Master of Architecture program, which he led for eight years.
Before joining the staff at the AA, which has a reputation as one of the world's most prestigious architecture schools, he worked as a project architect at Zaha Hadid Architects, founded London firm desArchLab, and practised as an architect and planner in New York.
Portrait of Brett Steele is by Tim Brotherton.