Try oven cleaner. Test it on a small spot first before doing the whole thing.

If that doesn't work there are stone cleaning products out there. Go into a stone/tile store or a stone yard with your picture and ask them for a recommendation on a product.

Thank you for the oven cleaner suggestion, Xanndra. It worked very well. I will post a new photo when finished.

I had tried a cleaner recommended by the chimney sweep we used. It worked okay, but not much better then soap and water. I think it just cleaned off the surface dust and not the soot.

Glad I could help. That's what 10 years experience in this business will get you--Oven cleaner!

Will the oven cleaner work on a brick fireplace?

Yes. Again, test it on a small area first to see if there is any discoloration or other problems.

I tried Quick n Brite on my brick fireplace to remove the soot and absolutely loved it! I could not believe the results! I have tried various other products to remove soot and creosote that did an okay job but there was always a reside still left behind (and many of the products were so toxic I wasn't wild about having them in an area where I would be lighting a fire soon!) I was recommended Quick n Brite by a friend because it is a safe product without chemicals so I didn't have to worry about my children or pets (which I loved). I put the paste on my fireplace with a stiff brush, let it sit about 30 minutes then came back and wiped it off with a damp terry cloth towel. It was like brand new, I have not seen it that clean in 20 years and I did not have to scrub my arms off either! I have been recommending Quick n Brite to all my friends since then and everyone I have shared mine with has been very pleased as well. Great product.

Here is a link that might be useful: Quick n Brite

A lemon cut in half does a great job. Just rub it, rinse with water, slice the soot off the lemon half and go at it again. Safe for the environment, and it works. https://www.houzz.com/discussions/my-lemon-cleaning-miracle-excess-lemons-dsvw-vd~2892619