Manipulation of the magnetization of a perpendicular ferromagnetic free layer by spin-orbit torque (SOT) is an attractive alternative to spin-transfer torque (STT) in oscillators and switches such as magnetic random-access memory (MRAM) where a high current is passed across an ultrathin tunnel barrier. A small symmetry-breaking bias field is usually needed for deterministic SOT switching but it is impractical to generate the field externally for spintronic applications. Here, we demonstrate robust zero-field SOT switching of a perpendicular CoFe free layer where the symmetry is broken by magnetic coupling to a second in-plane exchange-biased CoFe layer via a nonmagnetic Ru or Pt spacer. The preferred magnetic state of the free layer is determined by the current polarity and the sign of the interlayer exchange coupling (IEC). Our strategy offers a potentially scalable solution to realize bias-field-free switching that can lead to a generation of SOT devices, combining a high storage density and endurance with a low power consumption.