'azerbaijanese' is formed from the place-name 'Azerbaijan' plus the English demonym/adjectival suffix '-ese', which ultimately derives from Italian '-ese' and Late Latin '-ensis' meaning 'originating in'.

'Azerbaijan' itself comes from Persian 'Āzarbāyjān' (Middle Persian), which historically is linked to the Old Iranian/Medo-Persian name related to 'Atropates' (Greek), and the modern English form was adapted into demonyms like 'azerbaijanese' by adding the suffix '-ese'.

Originally a place name, the formation with '-ese' came to mean 'from or relating to Azerbaijan' and is now used as an adjective or demonym (and occasionally to refer to the language or people collectively).