1. Open the image that contains the texture that you're going to use to create your brush. Here's mine, but scaled down a bit:

2. You'll likely be working with a single-layer file at the point, and it'll be your "background" layer, so you'll need to duplicate it. You can't apply a gradient to a background layer. To duplicate it, right click on the layer in your layers palette and choose "duplicate layer" - like so:

3. Brushes aren't made in color, and so to give us a better idea of what the brush will look like, let's desaturate it. That also makes it easier if you decide you want to invert colors or any such thing later on, too. To do so, on the top menu, click Image > Adjustments > Desaturate (Hotkey: Shift+Ctrl+U - Mac: CMD+Shift+U).

4. Select White as your foreground color and black as your background color. Your colors palette should look like this:

5. Now, making sure that the DUPLICATED layer is selected, click on the layer style button at the bottom left of the layers window. Select "Gradient Overlay" as you see here:

6. These are the settings you're going to use. Make sure that you select a radial style, which will look like a black dot in the middle of a white screen. Then change the blend mode to "screen". I've made the scale about 90% or so because I want to make absolutely sure that there's no "chopping off" of the gradient at the edges. If your image isn't absolutely square, sometimes that can happen if you leave it at 100%.

Tip: At this point, if you don't like the selection, you can play around with several features. Change the scale. Unclick the "Align with Layer" feature and then click on the image itself and drag your mouse around. The selected circle moves! This way, you can get different selections and areas of the same image.

7. Almost done! Now, you just need to create your brush. On the top menu, click Edit>Define Brush Preset and you're done! If you're not sure how to create and save brush sets, please check out my tutorial on doing so here.

8. Here's what the brush looked like:

9. Here's what I did with my new brush. You can overlap the edges to create a seamless texture. You can use it in different sizes as well as mix up different textures to create all kinds of results!

10. Congratulations! You've made your own texture brush.