A detailed model for the origin of the Orion and Monoceros cloud complexes is presented, showing that a single high-velocity H I cloud-galaxy collision can explain their main observed features. The collision generates massive shocked layers, and self-gravity can then provide the conditions for the transformation of these layers into molecular clouds. The clouds formed by the collision maintain the motion of their parental shocked gas and reach positions located far away from the plane. According to this model, both the Orion and Monoceros complexes were formed some 60 million yr ago, when the original shocked layer was fragmented by Galactic tidal forces. 52 references.