This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.