Wordorigins.org

The word has been around since the fourteenth century. It comes from the Middle Dutch verb busen, meaning to drink heavily, and first appeared in English as a verb spelled bouse. This is from a satirical poem titled Heil Seint Michel, dating to sometime before 1325:

Hail ȝe holi monkes...Late and raþe ifillid of ale and wine! Depe cun ȝe bouse.
(Hail the holy monks…Slowly and before long filled with ale and wine! Deeply can they booze.)

And from Spenser’s 1590 The Faerie Queene, I.iv.22:

And in his hand did bear a bouzing can,
Of which he supt so oft, that on his seat
His dronken corse he scarse upholden can.

Folklore has it that this term for liquor comes from a Philadelphia distiller named E.C. Booz who prospered around 1840 by selling a popular spirit in bottles shaped like a log cabin. This is not correct. In addition to the British citations dating back to the fourteenth century, it has been in use in America since the early eighteenth century. Benjamin Franklin used the term boozy from 1722 and Noah Webster’s 1828 dictionary has entries for boose and bouse meaning “to drink hard; to guzzle,” and for boosy meaning “a little intoxicated; merry with liquor.”

(Source: Oxford English Dictionary, 2nd Edition; Middle English Dictionary; Historical Dictionary of American Slang; Noah Webster’s American Dictionary of the English Language)