I'm not sure there's much more to add than what has been said in the two excellent answers you've already received. So maybe to emphasise how not to give positive reinforcement when removing him from a chair/situation: pick him up from behind, not facing you, and keep him away from your body, like you might move an object. It's neutral, not positive, not negative. No talk except perhaps, "No climbing on chairs, please." Repeat until he gives up. If he thinks it's a game, make sure he doesn't see you smile or chuckle. Repeat as often as necessary.
He'll probably get frustrated and start to cry unless you provide something interesting for him to climb on. Thick foam pads on the floor that can be configured different ways are safe, and they're fun!
You can make climbing on the couch more interesting by putting attractive toys on the top back, or attach a slide to your couch. You might want to put pillows on the floor nearby in case he falls off.
Or you can let him climb up on the table (supervised of course). The up side to this is that it reinforces more skills than the alternatives; balance, coordination, agility and strength are all enhanced the harder it is to accomplish the climb. Make it a rule that he can only climb with a parent present. If he's not talking much yet, don't worry, he will understand what you're saying (even if he doesn't obey). Make sure he knows how to climb down off a chair by practicing so you can ask/tell him "No climbing chairs without Mommy or Daddy", and if you're really brave, teach him to climb off the table safely as well. At 2 years of age, children are old enough to understand and learn these concepts and behaviors.
My kids were allowed to climb everything (well, not bookcases or things that could fall on them, though these were all affixed to the walls), but I made sure they knew how to get down safely. That way, my heart didn't race as often as it might otherwise. ;)