Combine kielbasa, carrots, celery and onion in 4-quart saucepan or Dutch oven. Cook over medium heat, stirring occasionally, until vegetables are crisply tender (8 to 12 minutes).
Add all remaining ingredients. Continue cooking, stirring occasionally, until mixture comes to a full boil (2 to 3 minutes). Reduce heat to low. Cook until vegetables are tender (20 to 25 minutes).