Migrating birds fly thousands of miles or more, often without visual cues and in treacherous winds, yet keep direction. They employ for this purpose, apparently as a powerful navigational tool, the photoreceptor protein cryptochrome to sense the geomagnetic field. The unique biological function of cryptochrome supposedly arises from a photoactivation reaction involving radical pair formation through electron transfer. Radical pairs, indeed, can act as a magnetic compass; however, the cryptochrome photoreaction pathway is not fully resolved yet. To reveal this pathway and underlying photochemical mechanisms, we carried out a combination of quantum chemical calculations and molecular dynamics simulations on plant (Arabidopsis thaliana) cryptochrome. The results demonstrate that after photoexcitation a radical pair forms, becomes stabilized through proton transfer, and decays back to the protein's resting state on time scales allowing the protein, in principle, to act as a radical pair-based magnetic sensor. We briefly relate our findings on A. thaliana cryptochrome to photoreaction pathways in animal cryptochromes.