An analytical solution to Brownian coagulation of fractal agglomerates in the continuum regime that provides time evolution of the particle size distribution is presented. The theoretical analysis is based on representation of the size distribution of coagulating agglomerates 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 spherical particle solution previously obtained by K. W. Lee (J. Colloid Interface Sci. 92, 315-325 (1983)). The results show that the mass fractal dimension has a significant effect on the size distribution evolution during coagulation. When the obtained solution was compared with numerical results, good agreement was found. The self-preserving size distribution of nonspherical agglomerates is discussed.