Green’s Dictionary of Slang

well-dressed, smart, respectable.

1859, 1860		Hotten Dict. of Modern Sl. etc.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 251/1: George and his two fellow-labourers were ‘square-rigged’ – that is, well-dressed.
1873		Sl. Dict.
1908		A.N. Lyons Arthur’s 239: ’Twas a great, gentle, square-rigged mariner.
1925		S. Lewis Arrowsmith 154: Robert was a square-rigged, swart, tempestuous boy.