Although the Internet of Things (IoT) can increase efficiency and productivity through intelligent and remote management, it also increases the risk of cyber-attacks. The potential threats to IoT applications and the need to reduce risk have recently become an interesting research topic. It is crucial that effective Intrusion Detection Systems (IDSs) tailored to IoT applications be developed. Such IDSs require an updated and representative IoT dataset for training and evaluation. However, there is a lack of benchmark IoT and IIoT datasets for assessing IDSs-enabled IoT systems. This paper addresses this issue and proposes a new data-driven IoT/IIoT dataset with the ground truth that incorporates a label feature indicating normal and attack classes, as well as a type feature indicating the sub-classes of attacks targeting IoT/IIoT applications for multi-classification problems. The proposed dataset, which is named TON_IoT, includes Telemetry data of IoT/IIoT services, as well as Operating Systems logs and Network traffic of IoT network, collected from a realistic representation of a medium-scale network at the Cyber Range and IoT Labs at the UNSW Canberra (Australia). This paper also describes the proposed dataset of the Telemetry data of IoT/IIoT services and their characteristics. TON_IoT has various advantages that are currently lacking in the state-of-the-art datasets: i) it has various normal and attack events for different IoT/IIoT services, and ii) it includes heterogeneous data sources. We evaluated the performance of several popular Machine Learning (ML) methods and a Deep Learning model in both binary and multi-class classification problems for intrusion detection purposes using the proposed Telemetry dataset.