Rheotaxis and migration of cells in a flow field have been investigated intensively owing to their importance in biology, physiology and engineering. In this study, first, we report our experiments showing that the microalgae Chlamydomonas can orient against the channel flow and migrate to the channel centre. Second, by performing boundary element simulations, we demonstrate that the mechanism of the observed rheotaxis and migration has a physical origin. Last, using a simple analytical model, we reveal the novel physical mechanisms of rheotaxis and migration, specifically the interplay between cyclic body deformation and cyclic swimming velocity in the channel flow. The discovered mechanism can be as important as phototaxis and gravitaxis, and likely plays a role in the movement of other natural microswimmers and artificial microrobots with non-reciprocal body deformation.