Actually, according to Wikipedia the first official Elseworlds title was GOTHAM BY GASLIGHT (1989), written by Brian Augustyn, with art by Mike Mignola and Craig Russell. While listed as the first Elseworlds, it still didn't have the Elseworlds logo on the cover.

Setting Batman in 1889, in pursuit of Jack the Ripper, who has come from London and begun murdering women in Gotham. With some interesting twists that weave it into the Batman continuity.

I was unaware there was a sequel to it until I read the Wikipedia listing.