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The International Residential Code states:
Surface drainage shall be diverted to a storm sewer conveyance or other approved point of collection that does not create a hazard.
Lots shall be graded to drain surface water away from foundation walls. The grade shall fall a minimum of 6 inches (152 mm)within the first 10 feet (3048 mm).
Where lot lines, walls, slopes or other physical barriers prohibit 6 inches (152 mm) of fall within 10 feet (3048 mm), drains or swales shall be constructed to ensure drainage away from the structure. Impervious surfaces within 10 feet (3048 mm) of the building foundation shall be sloped a minimum of 2 percent away from the building.
You most certainly can place a concrete overlay on your patio and slope it to drain away from your house. Just make sure you place a flexible joint sealer in the crack between the new concrete and your foundation wall.
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I would fill the gap between the stone patio and the foundation wall with concrete at a more exaggerated slope to make sure no water pools along the wall. You need to provide a premolded joint filler (like you may see on the edges of sidewalks) up against the foundation wall before you pour your concrete. Leave it slightly recessed so that you can seal the joint with flexible sealer.
Another issue I see are all of the joints between your patio stones. All of those joints allow water to freely enter the ground around your home. Those need to be filled with clear, flexible sealer.
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