Welcome to rubber-band baby hood. Kids will go out and explore new things, but inevitably will snap back to Mom and Dad's legs like a rubber band.
My son is 4 1/2 and my daughter is 16 months. Both walked independently before their first birthday. I feel your pain, literally. :) There are a couple of things that you can to to help all of you.
1) Start walking with him holding on to both fingers, then gradually pull one finger out of his grasp so he's only holding one. This worked with both my kids when Dad would walk with them (Dad is over 6 feet tall).
2) Sit on the floor opposite your hubby with your feet touching and have your son walk back and forth between you two. My daughter loved this, especially towards me. She's such a Mommy's Girl.
Your son has learned a new skill, and wants the reassurances of Mom and Dad that his world is still on an even keel. Kids do this often. I forget the real name of it, but it's just like a rubber band or a bungee cord. They go out and out and out to explore, then they snap back to you as parents and stick close by for a while, then repeat cycle.
Congrats on your walker, he'll be running before you know it!