Ultrasound imaging has recently been introduced as a sensing interface for joint motion estimation. The use of ultrasound images as an estimation method is expected to improve the control performance of assistive devices and human--machine interfaces. This study aimed to estimate continuous wrist joint angles using ultrasound images. Specifically, in an experiment, joint angle information was obtained during extension--flexion movements, and ultrasound images of the associated muscles were acquired. Using the features obtained from ultrasound images, a multivariate linear regression model was used to estimate the joint angles. The coordinates of the feature points obtained using optical flow from the ultrasound images were used as explanatory variables of the multivariate linear regression model. The model was trained and tested for each trial by each participant to verify the estimation accuracy. The results show that the mean and standard deviation of the estimation accuracy for all trials were root mean square error (RMSE)=1.82 $\pm$ 0.54 deg and coefficient of determination (R2)=0.985 $\pm$ 0.009. Our method achieves a highly accurate estimation of joint angles compared with previous studies using other signals, such as surface electromyography, while the multivariate linear regression model is simple and both computational and model training costs are low.