One-dimensional transient groundwater flow from a divide to a river in an unconfined aquifer described by the Boussinesq equation was studied. We derived the analytical solution for the water table recession and drainage change process described with a linearized Boussinesq equation with a physically based initial condition. A method for determining the average water table in the solutions was proposed. It is shown that the solution derived in the form of infinite series can be well approximated with the simplified solution which contains only the leading term of the original solution. The solution and their simplification can be easily evaluated and used by others to study the groundwater flow problems, such as drainage and base flow estimation, in an unconfined aquifer.