Jeremy Annear was born in Exeter in 1949. After school he attended Exeter College of Art where he studied painting and printmaking. Following this he trained to teach at Exeter University Rolle College. In 1987 he moved to Cornwall to spend his time painting, and shortly after moving he became a member of the Newlyn Society of Art (NSA) (of which he became a committee member) and the Penwith Society of Artists. He also served on the council of management of the Newlyn Gallery.
Annear was awarded a DAAD stipendium in 1991, after which he lived in Germany for two years. His work was shown in exhibitions in Berlin, Leipzig, Worpswede and Bremen during this time, and he was also selected to mount a solo exhibition at the international Celtic Festival in L'Orient France. Annear spent an extended length of time painting in Sydney, Australia, in 1993 before returning to the UK. On his return he converted and developed a derelict former chapel and Sunday school where he now lives with his wife, the painter Judy Buxton, and their youngest daughter.