1942, American English slang, the first element probably a nonsense reduplication of suit (cf. reet pleat, drape shape from the same jargon).
A man's suit with a jacket having very wide lapels, heavily padded shoulders, and many-buttoned sleeves, with very high-waisted trousers full in the leg and tapering to narrow cuffs •Such garments were worn as symbols of status and defiance, esp by urban black hipsters and Los Angeles Chicanos: Some were garbed in short sleeve shirts, others in zoot suits/ Jelly got into his zoot suit with the reet pleats
[1942+; origin unknown; probably in essence a rhyming phrase of the sort common in black English and slang; perhaps related to other jive and cool-talk terms like vootie]