Absolutely YES. I hate running but it works better for anxiety than anything, in terms of immediate relief. Just put on your shoes and run. Get exhausted and your mind will relax. Power yoga has helped over the longer term, but is not as quick, it's more like prevention.
Dancing is hella therapeutic as well, can really help you bring up and process emotions, and if you can do it to exhaustion, works like running does but with the added advantage of engaging your mind while doing it, so you don't think as much.
I have relied on exercise to manage anxiety for about 30 years now. It does absolutely work.
ETA: I don't know if it would help depression and it didn't solve my mom's bipolar issues, she was always fit. Nothing is magic. But for 'simple' anxiety I have not found anything to work better than physical exercise to exhaustion. Get tired, sleep better, feel more relaxed and grounded.