The best solution would be to buy a tuba stand. It sits on the ground between your legs and has a curved portion that rests right in front of your chair where you place the tuba:
Is there a reason you feel that you're "supposed" to sit at the front of the seat? I'm a tuba player myself, and I sit at the back of the chair with the tuba sitting on the chair. Plenty of great tuba players do this, so don't be afraid to keep doing so! As long as you have a straight back and relaxed neck/shoulders and can breathe the way that the tuba requires, you should feel free to sit however you like.
Lastly, playing tuba can be a really unnatural thing. If you want to transition to having the tuba on your legs, feel free to switch it on and off your leg during the course of your playing. As the weeks go by, you'll become more accustomed to it, you'll build the necessary muscles, and the pain should go away.