The collection of 16 outfits worn during last year's series are housed in Woburn Abbey.
A Charleston dress worn by winner Caroline Flack and Pixie Lott's Viennese Waltz outfit are among those on display.
The 13th series of the BBC One programme is due to air next month.
Vicky Gill, a costume designer for the show, said she hoped visitors would revel in seeing the dresses up close.
She said: "I've been working on designing the Strictly dresses since the second series in 2005, and it never tires.
"It involves a lot of hard work, but it's all worth the effort as we begin to prepare for yet another series of fun, fantasy and glamour."
The exhibition runs until 1 November.
An exhibition of "fantastic costumes" worn by Strictly Come Dancing contestants and professionals has opened to the public in Bedfordshire.