Cheliax does not do anything as simple as 'surrender'. There is no peace treaty; the one person with legal authority under the old regime to sign such a thing has had her soul trapped in a gem. There is no ceasefire agreement; fighting ends gradually, and then all at once, as cities surrender and individually powerful people head to the Worldwound to register as independent adventurers under the treaty and the mundane troops quickly realize which way the wind is blowing. The Chelish army does not really surrender either; it just ceases to exist.
The end of Infernal Cheliax, then, comes in an announcement by the office of the Church of Abadar responsible for arbitration of the Worldwound treaty, broadcast by radio across Avistan and beyond, that in their estimation the rule of Cheliax for treaty purposes has passed to Lord Marshal Alexeara Cansellarion, commander-in-chief of the forces called the Glorious Reclamation; in response to which Cansellarion makes his own proclamation accepting interim legal authority for the country, and immediately thereafter banning the preaching of the faith of Asmodeus and freeing all slaves within its borders. A great many of the old regime's nobility have already fled to Absalom with their slaves but those that were slow to update about the progress of the war are largely arrested on their way out.
(Those who simply comply with the proclamation and free their slaves will not be bothered, though they probably won't be permitted to continue to hold titles. They'll even be compensated for the loss of their 'property', though at a small fraction of its assessed value.)
(There aren't very many of these.)
The new Grand High Priest of Asmodeus orders all Asmodean clerics to join him at the Worldwound, which they mostly do. Cansellarion's army doesn't stop them from leaving; it might be satisfying for every village to try its priest for his or her crimes, but it wouldn't really be Lawful.
And there are celebrations, of course; not so much within Cheliax itself, which is still too wary and too wounded to celebrate its freedom the way it should; but at the Abadarans' announcement there are fireworks lit in Absalom and Sothis and Oppara, to say nothing of Vellumis and Almas and Azir, and people rejoice to hear the news in far more distant places than those.