Drain and rinse the chickpeas and cannellini beans thoroughly under cold water and transfer to a large mixing bowl.
Add the diced cucumber, halved cherry tomatoes, finely diced red onion, sliced olives, and chopped parsley to the bowl.
In a separate small vessel, whisk together the olive oil, lemon juice, dried oregano, salt, and black pepper until the dressing is emulsified.
Pour the vinaigrette over the bean and vegetable mixture.
Gently fold in the crumbled feta cheese to prevent excessive breaking.
Toss all ingredients until evenly coated with the dressing.
Serve immediately or refrigerate for 30 minutes to allow the flavors to meld.