'cleave' (both senses) has Old English origins. The sense 'to split' comes from Old English 'clēofan' (or 'cleofan'), related to Proto-Germanic '*kleubaną' meaning 'to split, cleave'. The sense 'to cling/adhere' comes from Old English 'clifian', related to Proto-Germanic '*klibjaną' meaning 'to stick or cling.'

'cleave' (split) developed from Old English 'clēofan' into Middle English forms such as 'cleven'/'cleven' and later modern English 'cleave'; alternatively, irregular past forms like 'clove' and 'cleft' arose in Middle English. The 'adhere' sense came from Old English 'clifian' and evolved through Middle English into the modern verb 'cleave' with its regular past 'cleaved' and usage with 'to'.

Initially the roots denoted physically splitting ('clēofan') and sticking ('clifian') separately; over time English preserved both senses under the single spelling 'cleave', so the word now has opposite meanings ('to split' and 'to cling').