It is known that the transient behaviors of traditional adaptive control may be very poor in general, and that the adaptive control designed based on switching between multiple models is an intuitively appealing and practically feasible approach to improve the transient performances. This paper proves that for a typical class of linear systems disturbed by white noises, the multiple model based least-squares adaptive switching control is stable and convergent, and has the same convergence rate as that established for the standard least-squares-based self-tuning regulators. Moreover, the mixed case combining adaptive models with fixed models is also considered.