Place potatoes in a large pot and add enough cold water to cover by 1 inch. Bring to a boil over high heat, reduce to medium-low and simmer until potatoes are easily pierced with a fork, 30 minutes. Drain; slightly cool.
Cut potatoes in half and place in a large bowl. Add onion and celery. In a separate bowl, mix mustard with vinegar, mayonnaise, relish, salt and pepper. Pour over potatoes and gently stir to mix. Serve at room temperature or chilled.