Sauté chopped onion and celery in butter in a large skillet until vegetables are tender. Place vegetables and artichoke hearts in container of an electric blender; process until smooth.
Place flour in a large Dutch oven. Gradually add chicken broth, stirring until smooth. Cook over medium heat, stirring constantly, until thickened and bubbly. Stir in artichoke mixture; cook over medium heat until bubbly. Add milk, salt, and pepper; heat thoroughly. (Do not boil.) Serve warm or chilled in individual soup bowls.