Adams was born in Bristol, England. His parents are both teachers from coal mining families in the South Wales Valleys and the family moved to Lodge Hill in Caerleon in the mid-60s. He was later educated at the Welsh School of Architecture in Cardiff and he first started working for the former Greater London Council before getting a place at the Architectural Association in London. After graduating, he spent 15 years working in the practice of Will Alsop in London, where he worked on the North Greenwich tube station, next to the Millennium Dome. He returned to Wales in 1998. He later claimed he returned to Wales because London was "very inward-looking and self-regarding", while Wales was facing the "exciting time" of devolution during the late '90s.