Formation of solar filament channels by photospheric magnetic reconnection is considered. A magnetohydrodynamic model for magnetic merging, driven by converging convective motions in the photosphere, is presented. Evolution of the axial magnetic field in a channel is analyzed. An exact time-dependent analytical solution for the field profile in a steady stagnation-point flow is derived. The maximum magnetic field in the channel is determined, and its dependence on the reconnection inflow speed is discussed. The quantitative results show that the maximum axial magnetic field in a forming channel is an indicator of the photospheric reconnection rate, in agreement with recent solar observations and laboratory experiments.