Get a cat harness– they can probably slip out of a dog one. You can find them in most cat collar sections of a pet store.
Put it on him one day WHILE YOU’RE HOME to keep an eye on him. He may not move for a long, long time, haha– it feels like being scruffed, so a lot of cats just freeze at first. Eventually, he’ll figure it out and start slinking around the house, and then walking and then hopefully he’ll act normal. Try and keep him in an open area where you can watch him– i.e., indoors in the living room, and close the bedroom doors. The reason you need to be there is so he doesn’t panic (or even just run under the bed or somewhere else) and get the harness stuck on something.
Once he’s moving around normally with the harness on (which could take hours, days, or even weeks depending on how long your sessions are), you can attach the leash. It will take him some time to get the idea that now he CAN’T go everywhere he wants to, but eventually he’ll learn. Practice “walking” him around your house, then your yard, and when he moves forward with you (which doesn’t sound like it will be an issue since he already follows you everywhere) and stops with little resistance, he’s probably ready to go for real walks.
He may take a little time to get used to the weight of the leash on his back, too, FYI– in other words, he may regress to slinking or freezing again, but just keep doing it and he should get used to it. If he doesn’t like walking with you with the leash and harness at first, you can try to coax him forward a few steps with a treat, reward him, and then stop for the day. Always work with direct training in short, positive sessions and always end on a good note to keep the experiences positive for him.
Cats are a special breed, and they may not always perform. You also can’t “punish” them into working for you as is unfortunately popular with dogs. Be patient and feel free to ask me any questions you might have and I hope this helps (and works!).
Relevant: I’ve been working with animals all my life, including exotic animals, and have trained everything from cats to horses.