بسم الله الرحمن الرحيم
Yes! It is mandatory for the validity of oath to be uttered verbally. According to Shariah, oath does not come into effect merely by making intention in the heart. In such case if one goes against it then according to Shariah there is no kaffarah. (See: Shami 5:473, pub. Zakaria)
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.