Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Add vegetable broth, diced tomatoes, kidney beans, cannellini beans, pasta, zucchini, carrots, and celery to the pot. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until pasta is tender.
Stir in cooked meatballs and parsley. Season with salt and pepper to taste.