Is the new location of his litterbox private enough? Some cats don't like to use the box if there is a lot of traffic around it.
Outdoor cats may be even fussier about this requirement. If the box is in the middle of the room ,try putting it close to the wall so it seems more secure to him.
Does the new location mean your cat may have to pass closely or be in contact with your dogs to get to it? That could also make him hesitant to use it.
Cats are also very much creatures of habit and really dislike change. If it's impossible to leave your cat's box in it's original location, you might try locking him in at night in the room his box is in, until he gets used to using it there.
I had to lock my last indoor/outdoor cat up every night for 18 years, or he would wake us up at 3:00 a.m. without fail!
I don't know how old your cat is, but hopefully he is young enough to make the switch without too much trouble.