Help creating a blurred edge for fog of war

Hey All,

I'm working on a fog of war implementation for my 2d, tile-based rts game. At the moment, all it is is a layer of black tiles on top of the original ones, and each tile that is within a certain radius of the player will be cleared. I posted a video below.

The only problem is that the edges of the fog of war are too sharp. Is there any way I can make it a smoother transition between the black tiles and the regular ones? Maybe make it a blurred edge like the one in the below image?