The cats who call the Hemingway House in Key West home are all safe and accounted for after the bulk of Hurricane Irma spared the island city ... TMZ has learned.

Staff members that work at the Hemingway House tell us all 55 cats -- and the people who stayed behind to care for them -- are a-okay at the property ... which itself is still standing and suffered no major structural damage.

We're told all 10 Hemingway occupants, including manager Jacque Sands, lucked out big time since Irma left significantly less destruction than in the other Keys. Sources tell us while there are a few trees down on the estate, everything else at the house appears to be fine.

The Hemingway House also avoided major flooding. A source at the National Weather Service tells us Key West only saw a water surge of about 3 feet as opposed to the 15-20 feet anticipated throughout the Keys as Irma approached. We're told Key West was in the eye wall -- the strongest part of the hurricane -- for 2 hours. Water has begun to recede as Irma moves north.

As a result, those at the house are not currently inundated by water unlike Miami -- but are staying inside until winds die down.

As for those 6-toed cats ... talk about nine lives, huh?