An analytical solution to the Brownian coagulation of aerosol particles in the low Knudsen number regime is presented which provides time evolution of the particle size distribution. The theoretical analysis used is based on representation of the size distribution of a coagulating aerosol with a time-dependent log-normal size distribution function and employs the method of moments together with suitable simplifications. The results are found in the form that extends the continuum coagulation solution that was previously obtained by Lee (J. Colloid Interface Sci. 92, 315 (1983)). The results show that the Knudsen number has a significant effect on the size distribution evolution during coagulation. In addition, it was confirmed that a self-preserving size distribution does not exist in the low Knudsen number regime. The obtained solution was compared with numerical results and good agreement was obtained. The present work represents the first analytic solution to the low Knudsen number regime Brownian coagulation problem.