Mix 1 cup chlorine bleach with 1 gallon warm water in a bucket. Do not add any other cleaning solutions, since mixing chlorine bleach with other household chemicals can cause toxic fumes.
Dip a stiff-bristled brush in the solution and scrub the wall. Moss has no roots so it comes off easily. The bleach solution will discourage regrowth.
Spray a large area with a power washer, rather than scrubbing it. Set the power washer on a low setting and spray across the wall at an angle, rather than blasting water directly into the joints. The stream from a power washer can damage bricks and stones if used incorrectly.