You've gotten some good advice already--I especially second the idea of encouraging him to "help" you whenever possible.
My middle child was this way as well. He was very demanding, high-needs for the first 2 years. In retrospect, we now know that part of the problem was a health issue we hadn't discovered: he was celiac and until we discovered this and changed his diet he almost always had a stomach ache which contributed to the clinginess and whininess a LOT.
But, health issues asside, the thing that helped us was to put him on my back in a baby carrier. I liked an Asian Style carrier called a Mai Tai which kept him close on my back and distributed his weight evenly on both shoulders and my hips. This way I had both hands free to work and he could have all the contact he so obviously needed.
Having this closeness when he needed it reassured him a lot and while we would have brief periods of time when he needed a lot of carrying he did become more sercure and independant before too long. Before we had even figured out his health issues he'd become a more independant little guy and was spending much less time on me and more time playing.
He's still my most demanding touch-needing child, but nothing like those first 2 years. I think some people thought he'd never be happy anywhere but with Mommy, and now he's a happy outgoing little extrovert who loves everybody.
Good luck. It's hard to be needed to that degree and easy to get frustrated and touched-out. Believe me, I know! I spent those first 2 years wishing he'd find some way to comfort himself that didn't involve being on *me*, pulling and twisting my hair, squeezing, pinching etc--being a human lovey is a tough job! But in retrospect it was all worth it to have such a sweet, happy, secure kid on the other side. It will happen for you, too!