Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low; simmer until tender yet still firm, about 20 minutes. Drain and refrigerate until cool, about 30 minutes.
Place eggs in a saucepan; cover with water. Bring to a boil, remove from heat, and let eggs stand in hot water for 15 minutes. Remove eggs from hot water, cool under cold running water; peel and dice eggs.
Chop potatoes and place into a large bowl. Stir eggs, celery, and green onions into potatoes; mix in mayonnaise and mustard. Season with salt and pepper.