Conventional Hardware Trojan (HT) detection techniques are based on the validation of integrated circuits to determine changes in their functionality, and on non-invasive side-channel analysis to identify the variations in their physical parameters. In particular, almost all the proposed side-channel power-based detection techniques presume that HTs are detectable because they only add gates to the original circuit with a noticeable increase in power consumption. This paper demonstrates how undetectable HTs can be realized with zero impact on the power and area footprint of the original circuit. Towards this, we propose a novel concept of TrojanZero and a systematic methodology for designing undetectable HTs in the circuits, which conceals their existence by gate-level modifications. The crux is to salvage the cost of the HT from the original circuit without being detected using standard testing techniques. Our methodology leverages the knowledge of transition probabilities of the circuit nodes to identify and safely remove expendable gates, and embeds malicious circuitry at the appropriate locations with zero power and area overheads when compared to the original circuit. We synthesize these designs and then embed in multiple ISCAS85 benchmarks using a 65nm technology library, and perform a comprehensive power and area characterization. Our experimental results demonstrate that the proposed TrojanZero designs are undetectable by the state-of-the-art power-based detection methods.