This quote from Garak to Ziyal in A Call to Arms to me implies that although Garak's exile from Cardassia wasn't his choice, it was actually his idea to live among the Bajorans, even if it wasn't ideal. I would guess that Garak requested and was granted asylum from the Bajoran government as he "sought shelter" among them.
But who granted him that shelter, and why wasn't it revoked by the Bajoran Government after the Cardassians left, especially given Bajor's distrust (at that time) of Cardassians?
My apologies for not answering your original question completely. I'm afraid like most I can only offer my own speculation with a basis on what we saw on screen. My take on it is this:
We know the Cardassians left the station in pretty bad shape (Emissary
) and that they also have a penchant for setting some pretty nasty booby traps behind (Civil Defense, Empok Nor
), and we can assume that the Bajorans felt that the station was a pretty valuable asset worth keeping. So I see our ever-resourceful friend Garak approaching the Provisional Government (or whoever is in charge of restoring the station) with a proposal that he would help the Bajorans find and bypass all the various booby traps (especially the ones designed to kill non-Cardies), grant Cardassian computer access, and the like in exchange for asylum and accommodation on the station. Having a Cardassian that they can make use of "just in case" reduces any potential future problems (such as the issues in Civil Defense). So it was not an ideal arrangement for either party, but one that served both.
Or if you prefer your Garak to be a bit more sinister, with his background in the Obsidian Order and inside knowledge Garak was probably aware of many secret collaborators in the upper ranks of the government that the Bajorans themselves didn't know about and used that leverage to pull whatever strings he needed to secure his place on the station.