Raw carrots and raw celery are perfectly safe and healthy for dogs to eat.
Although it's best to cut the raw carrots and celery up in bite sized pieces to help the dogs stomach with digestion of the raw carrots and raw celery.
Also remove the leaves from the raw celery before giving it to the dog as the leaves of the celery could cause digestion issues.
The carrots and celery are good for your dogs health and even some dog foods contain celery and carrots that are mixed in with the food where you cannot see it.
Just avoid overfeeding the dog too much celery and carrots as it could lead to diarrhea but in moderation the celery and carrots are good for dogs to eat.