Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 15 to 20 minutes. Drain, cool, and chop into 1-inch cubes. Transfer to a large bowl.

Meanwhile, place eggs in a medium saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove eggs from hot water; cool, peel, and dice.

Whisk mayonnaise, green onions, milk, vinegar, salt, and black pepper together in a bowl until well combined; pour over potatoes. Add eggs and celery; mix well.

Cover the bowl with plastic wrap; chill in the refrigerator before serving, about 2 hours.