'yay' is a colloquial alteration of 'yea,' which comes from Old English 'g
2b1' meaning 'yes' or 'so'.

'g
2b1' (Old English) changed into Middle English 'yea', which later developed the colloquial variant 'yay' used as an exclamation and informal noun.

Initially it meant 'yes' or an affirmative vote; over time it broadened to include an informal exclamation of joy or triumph as well as the noun meaning 'an affirmative vote.'