The Founders' homeworld was the capital of the Dominion. At least two planets served this purpose.
First Founders' homeworld
The Founders' homeworld was the common designation for an M-class rogue planet located in the Omarion Nebula, in the Gamma Quadrant. The species of Changelings known as the Founders withdrew to this planet 10,000 years ago, abandoning whatever original worlds they occupied, to escape persecution by the solids. Odo and Major Kira Nerys visited the planet in 2371, when Odo was searching for his origins. The crew of the USS Defiant was also held here while the Vorta conducted an experiment to gauge the level of resistance to a Dominion invasion. (DS9: "The Search, Part I", "The Search, Part II")
Thirty percent of the planet's crust was destroyed by weapons fire from warships operated by the Cardassian Obsidian Order and the Romulan Tal Shiar in 2371, during the Battle of the Omarion Nebula. The Founders had previously evacuated the planet, and deliberately allowed the attack so as to ambush the two intelligence agencies and render them incapable of resisting the planned conquest of their respective empires. (DS9: "The Die is Cast")
Second Founders' homeworld
The new Founders' homeworld was also located in the Gamma Quadrant, though its exact coordinates were kept secret. In 2372, the Great Link appeared to cover much of the surface of this planet, leaving very little landmass. The Defiant was guided by the Jem'Hadar to this planet in 2372 when Odo was compelled to return to the Link to face judgment for killing another Changeling. (DS9: "Broken Link") Odo again returned to the planet after the end of the Dominion War in order to cure the morphogenic virus infecting the Link and convince them that the solids were no longer a threat to them. (DS9: "What You Leave Behind")