The Smart Grid is a new type of power grid that will use advanced communication network technologies to support more efficient energy transmission and distribution. The grid infrastructure was designed for reliability; but security, especially against cyber threats, is also a critical need. In particular, an adversary can inject false data to disrupt system operation. In this paper, we develop a false data detection system that integrates two techniques that are tailored to the different attack types that we consider. We adopt anomaly-based detection to detect strong attacks that feature the injection of large amounts of spurious measurement data in a very short time. We integrate the anomaly detection mechanism with a watermarking-based detection scheme that prevents more stealthy attacks that involve subtle manipulation of the measurement data. We conduct a theoretical analysis to derive the closed-form formulae for the performance metrics that allow us to investigate the effectiveness of our proposed detection techniques. Our experimental data show that our integrated detection system can accurately detect both strong and stealthy attacks.