Elongin A performs dual functions in cells as a component of RNA polymerase II (Pol II) transcription elongation factor Elongin and as the substrate recognition subunit of a Cullin-RING E3 ubiquitin ligase that has been shown to target Pol II stalled at sites of DNA damage. Here we investigate the mechanism(s) governing conversion of the Elongin complex from its elongation factor to its ubiquitin ligase form. We report the discovery that assembly of the Elongin A ubiquitin ligase is a tightly regulated process. In unstressed cells, Elongin A is predominately present as part of Pol II elongation factor Elongin. Assembly of Elongin A into the ubiquitin ligase is strongly induced by genotoxic stress; by transcriptional stresses that lead to accumulation of stalled Pol II; and by other stimuli, including endoplasmic reticulum and nutrient stress and retinoic acid signaling, that activate Elongin A-dependent transcription. Taken together, our findings shed new light on mechanisms that control the Elongin A ubiquitin ligase and suggest that it may play a role in Elongin A-dependent transcription.