The astronomer who published the velocity–distance law based on galaxy redshifts in 1929 was Edwin Hubble.
Hubble’s 1929 paper compared galaxy distances with their measured radial velocities and reported a roughly linear relationship: more distant galaxies generally appeared to be receding faster. That result became known as Hubble’s law and helped establish observational evidence for cosmic expansion.
The discovery involved more than Hubble alone. Vesto Slipher had measured the redshifts of many galaxies, providing much of the velocity data used in the developing picture. Georges Lemaître had also derived and published an expanding-universe relation in 1927. Hubble’s major contribution in this context was the influential 1929 observational analysis linking galaxy distance estimates to redshift-based velocities.
A common mix-up is to credit Hubble with discovering every part of the result. Slipher’s spectroscopy was crucial, and Lemaître’s earlier work anticipated the relation. Nevertheless, when a quiz asks who published the velocity–distance law in 1929, Edwin Hubble is the standard canonical answer. The law is now often called the Hubble–Lemaître law.