We had 2 dogs when we got the cat, they stayed well away from each other. Well dogs wanted to eat investigate the cat, cat stayed well away.
We have 4 dogs now. It works in that the dogs have now been trained to ignore the cat. The cat has chilled out a bit now he has realised he won't get eaten.
They both need areas away from each other. So the litter tray and cat food has to be probably upstairs where the dogs can't go. Cat needs access to high spaces, so on the bench, tables wardrobes etc to get higher than the dogs.
Next you need constant vigilance. If you are out and all animals are in the house, they must be locked apart. Get a dog gate for the stairs (taller than baby gate).
How well trained are your dogs? Will they stop and sit on command? Can you make them stay - and I mean properly, not for a bit then they wander off.
If not you need to work on this before you move. Mine were (they are working gun dogs so pretty well trained), and all I did was give the stop and sit command if the cat came near. I would then make them stay while I fussed the cat. They got the message quite quickly. Then I started to leave them to it. If they moved too quickly they were stoped and made to lie down. If they slowly approached without a hungry look in the eye, then I left them to it.
Now they just accept the cat as part of the scenery and largely ignore him. The cat rules the roost and will occasionally throw his weight around, will sit on the stairs and stop the dogs going up etc.
Be aware that as much as the dogs pose a threat to the cat, often unless the dog properly attacks a cat, the cat will do more damage to the dog, particuarly their eyes.
It won't be easy and a lot of it comes down to the nature of the animals. Keeping them apart will be the main thing.