Exercise is of course highly beneficial for overall health. However, some acne patients report a flare-up (especially on back and chest, i.e. skin areas covered with clothing) after sweating. Of course everybody is different, but in any case make sure to wash your skin directly after exercise to remove sweat, dirt etc., which could further clog pores. A foaming (non-creamy, non-oily) cleanser works best for acne prone skin.
Thinking about other areas of skin health, I can confirm however that exercise is beneficial for our skin. When we exercise, our skin’s blood circulation is boosted and with it its oxygen and nutrient supply. Exercise (especially interval and strength building exercise!) also induces release of human growth hormone, which has collagen building effects and great long-term anti-ageing effects.
Generally, I advocate interval and strength training over endurance exercise with regards to skin benefits, as in my personal experience chronic cardio (e.g. running for 60-90min.) can over time lead to a more pronounced loss of our (youthful!) facial heart shape (via flattening of the cheek fat pads) and might make you look older quicker than need be. If you compare the average sprinter to a marathon runner’s face, you will know what I mean!