Summer of 1994, between airing of "The Jem'Hadar" and writing of "The Search"
At the time that the Season 2 finale "The Jem'Hadar" had aired, the writers still did not know who the Founders would be, and therefore the idea of the Dominion had preceded the notion that its leaders would be Changelings.
It was decided that summer, independently by producer Michael Piller and showrunner Ira Steven Behr, that Odo's people would be the Founders.
This is according to Behr himself in the Season 3 DVD Special Features (segment: "The Birth of the Dominion and Beyond"). He said that he had been afraid to propose the idea to Piller because it seemed too "crazy", and then was pleasantly amused when Piller proposed it himself. They also debated whether to reveal immediately that the Founders are Changelings or to wait several years.
Interestingly, according to the book Captains' Logs Supplemental: The Unauthorized Guide to the New Trek Voyages, it was originally proposed during the very first planning meetings for DS9 that Odo may never discover his species, or that he might meet them and discover that he is their king.