The demand for Internet of Things services is increasing exponentially, and consequently a big number of devices are being deployed. To efficiently authenticate these services, the use of Physical Unclonable Functions (PUF) has been introduced as a promising solution that is suitable for the resource-constraint nature of these devices. A growing number of PUF architectures has been demonstrated mathematically clonable through Machine Learning (ML) modeling techniques. The use of ML PUF models has been recently proposed to authenticate the IoT objects. This procedure facilitates the scalability of the authentication process by reducing the storage space required for each device. Nonetheless, the leakage scenario of the PUF model to an adversary due to an insider threat within the organization is not supported by the existing solutions. Hence, the security of these PUF model-based enrollment proposals can be compromised. In this paper, we propose an enrollment solution that exploits a ML PUF model in the authentication process, called Water-PUF. Our enrollment scheme is based on a specifically designed black-box watermarking technique for PUF models with a binary output response. This procedure prevents an adversary from relying on the watermarked model in question or another derivative model to bypass the authentication. Therefore, any leakage of the watermarked PUF model that is used for the enrollment does not affect the correctness of the protocol. The Water- PUF design is validated by a number of simulations against numerous watermark suppression attacks to assess the robustness of our proposal