Place the potatoes into a 3-quart saucepan and add water to cover. Heat over medium-high heat to a boil. Reduce the heat to low. Cook for 10 minutes or until the potatoes are tender. Drain the potatoes well in a colander.
Stir the soup, mayonnaise, vinegar and black pepper in a large bowl. Add the potatoes, celery, green pepper, onions and eggs and toss to coat. Cover and refrigerate for 3 hours or overnight.