Using a fitness ball as a desk chair started when physical therapists began recommending it for those who had lower back pain, core instability, or posture problems. Since then, this practice has become quite common and even some workplaces advocate for their use.
By bouncing up and down slightly as you work, you can help build core strength as well as keep your legs moving. The movements you make at your desk regularly now force you to keep balanced on the ball will help to increase core strength. If you find you need to move around more and need mobility, there are fitness ball chair cradles that give the ball wheels while still giving you all the benefits of using an exercise ball as a desk chair.