Be patient. In the vast majority of cases, the hips stretch out in time. How much time depends upon your age and whether or not there is some hip joint pathology. It could take anywhere from a few weeks to a year or more. It’s well worth the wait. Once the hips become flexible, not only does posture improve when you sit, but also when you stand. You may also walk and run with a longer, smoother, and more upright stride. In general, the more flexible your hips, the less strain on your back.
For optimal hip positioning, make sure you are using the saddle stool at the proper height. Your body should be half-way between sitting and standing with a thigh-torso angle of about 135-degrees. If your hips are quite stiff, you may have difficulty positioning the seat high enough at first. Keep trying. It can take some time for hip joints to loosen.