This is how I grow sweet potatoes every year and it works great. Once you have growth like your picture, you cut them off near the tuber and stick them in moist soil and they are guaranteed to root and grow quickly.
If your soil outside is nice and moist you can stick the cuttings directly into the garden soil. Make sure at least a couple inches of stem is below the surface. They need a long growing season to bear fruit but if you're in the south you still have plenty of time.
