Since Blender now supports FBX format just fine, it is probably the easiest way how to approach bvh to fbx conversion, because the software can also work with character animation data from BVH files. You can actually find converters on GitHub based on Blender Python API that can be used the same way. Often done for models/animations for computer games (modding).
Of course the same should also be doable with other, commercial 3d modeling tools, such as 3ds max or DAZ Studio.