1. Place potatoes in a large pot and cover with water. Bring to a boil, then reduce heat and simmer for about 15 minutes, until tender. Drain and cool.
2. In a large mixing bowl, combine mayonnaise, mustard, celery, onion, relish, salt, and pepper.
3. Add the cooled potatoes and chopped eggs to the bowl. Mix gently until well combined.
4. Cover and refrigerate for at least 1 hour before serving.