Place the potatoes in a large saucepan with enough salted water to cover by 1 inch. Bring to a boil and cook until just tender, about 10 minutes. Add the green beans and cook until bright green, 3 to 4 minutes. Drain in a colander and let cool.
Meanwhile, in a large serving bowl, stir together the pesto, olive oil and vinegar. Add the potatoes, green beans, tomatoes and olives; toss. Season with salt.