Self-organization is a hallmark of all living systems [1]. In particular, coordinated cellular behavior, commonly orchestrated at the population level through reciprocal interactions among different cell species [2–4], regulates the spatial arrangement of specialized cell types to generate tissue patterning and form complex body layouts [5, 6]. The overwhelming complexity of living systems, however, makes deciphering the underlying mechanisms difficult and limits our knowledge of basic pattern-forming mechanism in vivo [7, 8]. A successful strategy is then to work with synthetic, engineered systems, in which cellular interactions can be more easily tailored and studied [9–13]. Here, we demonstrate a simple mechanism through which different populations of cells can self-organize in periodic patterns. Programmed population interactions are shown to lead to coordinated out-ofphase spatial oscillations of two engineered populations of Escherichia coli. Using a combination of experimental and theoretical approaches, we show how such patterns arise autonomously from reciprocal density-dependent activation of cellular motility between the two species, without the need of any preexisting positional or orientational cues. Moreover, by re-designing the interaction, the original out-of-phase spatial oscillation rhythm of the two populations can be accordingly turned into in-phase oscillations. The robustness and versatility of the underlying pattern-formation process suggest that it could both be generically encountered in nature, for instance in the complex bacterial ecosystems found in biofilms [14–16], and used to promote the mixing or demixing of active particles in a controlled way.