Once you have setup your material with the procedural noise, make sure your model has an UV.
Then go to Edit Mode.
In the UV Editor create a new texture, then in the Render panel, in the Bake section, in the Bake Mode drop down select Texture.
Set the margin to 4 or 5 and press the Bake button.
An example of this in the attached screenshot in which i used a voronoi procedural textural, a bit of normal value, a few lights and an ambient occlusion, then i set the Bake Mode to “Render” and clicked Bake, it created the texture on my UV
The only problem with this is that Blender is not able to antialias the baking process, so if you look closely to your obtained texture you should notice obvious aliasing edges everywhere things should be smoothly rounded.
a workaround on this is to create the new texture in Blender to be 4 times the size of the real texture you want (by example 20482048 if you want a 512512 final texture) and in an image editing program like photoshop or gimp or whatever else you use, rescale the texture to your desired dimension.
It will smooth all the ugly aliased edges created by Blender in the baked texture.