By default Photoshop uses the center of an object for the start of a radial gradient.
You simply need to ensure the Align with Layer option is ticked.
Just draw a circle and apply a radial gradient fill. That's all there is to it.

You can even use a Gradient Overlay Layer Style.

Videos
I've been using this method to "add glow" around lights. I duplicate the layer, then add a brightness layer. Using the gradient tool on the brightness layer, it initially goes from dark to light, then if I invert the layer mask, it gives a small glow around the light that fades out with the mask. Once I invert the mask though, I can't control how large the gradient is anymore, the slider/circle that adjusts its size goes away. Is there anyway to control the size of the circle after inverting?