Green’s Dictionary of Slang

(Can./US) the drinks are on the house!

1881		A.C. Grant Bush-Life in Queensland II 51: One of them shouting, ‘Belly up, boys! I’m in for this good thing,’ made his way to the bar.
1929		J. Tully Shanty Irish 171: ‘Bellies to the bar, men’ he called, ‘bellies to the bar.’ Soon all in the place were lined up at the bar for a drink.
1931		Ade Old-Time Saloon 105: [They] kept hanging around and waiting for some one to come in and order all present to ‘belly up to the bar,’ and the evening roysterers who were violently opposed to going home early.
1933		J. Conroy Disinherited 212: ‘Bellies to the bar!’ Jaspar whooped.