The new retro-style shirts go back to those worn in the days of John Toshack, with a round collar and a central badge.
The home kit is white with black trim, while the away colours go back to black with white trim replacing last season's red shirt.
The new shirts will be made by Italian suppliers Macron, and are ready for sale, however, with Swansea without a club shop or sponsor at present, it could be next month before they're made available to the public.
It is believed that a store will be shared with the Ospreys and will open at the new stadium before the visit of Fulham for Alan Curtis' testimonial match on July 23.
"We are governed by the contractors on this one and they have promised it will be open before the Fulham game," a spokesman said.
The Quadrant store is owned by former kit suppliers Bergoni and is expected to close on July 2.