Cell division is a fundamental process for both eukaryotic and prokaryotic cells. In bacteria, cell division is driven by a dynamic, ring-shaped, cytoskeletal element (the Z-ring) made up of polymers of the tubulin-like protein FtsZ. It is thought that lateral associations between FtsZ polymers are important for function of the Z-ring in vivo, and that these interactions are regulated by accessory cell division proteins such as ZipA, EzrA and ZapA. We demonstrate that the putative Escherichia coli ZapA orthologue, YgfE, exists in a dimer/tetramer equilibrium in solution, binds to FtsZ polymers, strongly promotes FtsZ polymer bundling and is a potent inhibitor of the FtsZ GTPase activity. We use linear dichroism, a technique that allows structure analysis of molecules within linear polymers, to reveal a specific conformational change in GTP bound to FtsZ polymers, upon bundling by YgfE. We show that the consequences of FtsZ polymer bundling by YgfE and divalent cations are very similar in terms of GTPase activity, bundle morphology and GTP orientation and therefore propose that this conformational change in bound GTP reveals a general mechanism of FtsZ bundling.