Place potatoes in a medium saucepan, cover with water, and bring to a boil. Reduce heat and simmer 20 minutes. Add beans; cook 1 1/2 minutes. Drain and rinse with cold water until cool. Cut potatoes into quarters; place potatoes and beans in a large bowl. Add tomatoes and onion; toss gently to combine.
Combine oil and next 5 ingredients (through pepper) in a small bowl, stirring with a whisk. Pour over potato mixture; toss gently to coat. Stir in parsley and olives just before serving.