There is a syndrome known as lower cross syndrome. This syndrome is the presentation of weak abdominal muscles and weak gluteal muscles with tight low back and hip flexor muscles.
Sitting for long periods of time can cause this syndrome. In addition to the lower cross syndrome developing, the hamstrings are likely to become shortened adding to the already painful achy back that many people experience during their day.
Sitting with your back slightly rounded causes your lower back muscles to be pulled and so they will try very hard to contract to keep you in a correct position. These low back muscles end up overworking, become tight and develop trigger points.
You back should have a normal inward curve that when sitting should be maintained. Having a chair that fits your body type is an option. Others have used fitness balls to sit on to strengthen the muscles of the core developing proper posture.
Stretching the low back muscles:
Gently pull your knees towards your chest and hold for 30 seconds. Bringing your head towards your knees will intensify the stretch so add this move as time goes on. Repeat the stretch 3 times. Variations include pulling one knee in at a time.