'anticyclonic' (and thus 'anticyclonically') originates from the combining form 'anticyclone', built from the prefix 'anti-' (Greek 'anti-', 'against, opposite') and 'cyclone' (from Greek 'kyklon'/'kuklos', 'circle, ring'). The adverb is formed by the adjective 'anticyclonic' + the adverbial suffix '-ally'.

'anticyclone' was formed in modern meteorological English from 'anti-' + 'cyclone' (where 'cyclone' came via New Latin/modern Greek from Greek 'kyklon' meaning 'whirl' or 'circle'); 'anticyclonic' then developed as the adjective, and 'anticyclonically' as the adverbial form.

Initially the components meant 'against/opposite' and 'circle/whirl'; combined they came to denote a weather system with rotation opposite to a cyclone. The modern usage specifically describes rotation and behavior associated with high-pressure systems.