Accurate measurement of inertial quantities is essential in geophysics, geodesy, fundamental physics and navigation. For instance, inertial navigation systems require stable inertial sensors to compute the position and attitude of the carrier. Here, we present the first hybridized cold-atom inertial sensor based on matter wave interferometry where the atomic measurements are used to correct the drift and bias of both an accelerometer and a gyroscope at the same time. We achieve respective bias stabilities of 7×10−7 m/s2 and 4×10−7 rad/s after two days of integration, corresponding to a 100-fold and 3-fold increase on the stability of the hybridized sensor compared to the force-balanced accelerometer and Coriolis vibrating gyroscope operated alone. The instrument has been operated under up to 100-times the Earth rotation rate. Compared to state-of-the-art atomic gyroscope, the simplicity and scalability of our architecture make it easily extendable to a compact full six-axis inertial measurement unit, providing a pathway towards autonomous positioning and orientation using cold-atom sensors.