The myth that the expansion of the Universe was discovered by Hubble was first propagated by Humason (1931). The true nature of this discovery turns out to have been both more complex and more interesting. ...These papers are convincing. The facts have been known for 80 years, so I don't know why these papers are necessary, but Hubble continues to be credited with Hubble's law, and as the leader of a great paradigm shift. Hubble's main accomplishment seems to have been that he convinced Einstein of the evidence, whereas Einstein had previously attacked Lemaitre for saying the same thing. The big bang was one of many things that Einstein was profoundly wrong about.
The first tentative steps toward the discovery of the velocity-distance relationship were made by Wirtz (1922, 1924) and Lundmark (1925). ...
Lemaître (1927) published a crucial paper that both established the expansion of the Universe and interpreted it as a consequence of the General Theory of Relativity. However, it is possible that Hubble (1929) was unaware of Lemaître’s 1927 paper on the expansion of the universe because it had been published in French in a rather obscure publication. Nevertheless it is puzzling that Hubble and Lemaître would not have discussed this problem when they were both attending the 1928 IAU meeting in Holland.
Update: A 24 Aug 2011 paper, Vesto Slipher and the First Galaxy Redshifts, says, "Priority in the discovery of the velocity-distance relationship may be shifting from Edwin Hubble to Georges Lemaitre".