Ideally, rehabilitation of neuromusculoskeletal impairments would involve repeated measurement of a patient’s movement capabilities and limitations, facilitating patient assessment throughout the treatment process. While optical motion capture systems are currently the most commonly used technology for measuring human movement, they are expensive and require a well-controlled indoor test environment, necessitating repeated patient visits to the clinic. Wearable inertial measurement units (IMUs) are a cheaper alternative that can measure human movement in any environment, but the state estimation methods commonly used to convert IMU measurements into joint kinematic data require numerical integration of noisy IMU data, resulting in significant integration drift. This study presents a novel integrationless method for measuring human movement with IMUs. The method must be used off-line and employs nonlinear optimization for state estimation, utilizes a physics-based kinematic model with joint constraints to provide the necessary theoretical relationships between IMU kinematics and joint kinematics, estimates joint positions, velocities, and accelerations simultaneously, and replaces numerical integration applied sequentially one time frame at a time with numerical differentiation applied over all time frames simultaneously. The method does not require IMU magnetometer data, calculation of IMU orientation in the global reference frame from IMU gyroscope data, or subtraction of the acceleration due to gravity from IMU accelerometer data. As an enhancement, the method also uses machine learning models to inform estimation of secondary joint kinematics that are not well defined by physics-based relationships alone. The method was evaluated quantitatively using experimental IMU and optical motion capture data collected simultaneously from the pelvis and lower limbs of a single healthy subject who performed walking, jogging, and jumping trials, where inverse kinematic results generated using the optical motion capture data were treated as the “gold standard” joint angle measurements. Without the machine learning enhancement, the proposed integrationless optimization method produced average root-mean-square (RMS) errors on the order of 3 degrees for walking, 6 degrees for jogging, and 12 degrees for jumping. With the machine learning enhancement, these errors were reduced to roughly 3 degrees for all three movements. In contrast, a standard unscented filter method produced average RMS errors of 18 degrees, 19 degrees, and 16 degrees for the same three movements, respectively. These findings suggest that the proposed integrationless optimization method for estimating joint kinematics from IMU data could potentially be used in place of an optical motion capture system for patient assessment situations where real-time measurement capability is not required.