We propose a first-principles approach for treating the unstable vibrational mode of transition states in solid-state diffusion. It allows one to determine a number of fundamental quantities associated with the transition state, in particular the enthalpy and entropy of migration and the characteristic vibrational frequency, along with their temperature dependences. Application to pure face centered cubic Al shows good agreement with available experimental measurements and previous theoretical calculations. The procedure is further applied in calculations of the migration properties of Mg, Si and Cu impurities in Al, and the differences among Mg, Si and Cu are discussed.