Cell division is tightly controlled in space and time to maintain cell size and ploidy within narrow bounds. In bacteria, the canonical Minicell (Min) and nucleoid occlusion (Noc) systems together ensure that division is restricted to midcell after completion of chromosome segregation1. It is unknown how division site selection is controlled in bacteria that lack homologues of the Min and Noc proteins, including mycobacteria responsible for tuberculosis and other chronic infections2. Here, we use correlated optical and atomic-force microscopy3,4 to demonstrate that morphological landmarks (waveform troughs) on the undulating surface of mycobacterial cells correspond to future sites of cell division. Newborn cells inherit wave troughs from the (grand)mother cell and ultimately divide at the centre-most wave trough, making these morphological features the earliest known landmark of future division sites. In cells lacking the chromosome partitioning (Par) system, missegregation of chromosomes is accompanied by asymmetric cell division at off-centre wave troughs, resulting in the formation of anucleate cells. These results demonstrate that inherited morphological landmarks and chromosome positioning together restrict mycobacterial division to the midcell position.