We propose a new reconstruction algorithm for photoacoustic and laser-ultrasound imaging based on reverse time migration (RTM), a time reversal imaging algorithm originally developed for exploration seismology. RTM inherently handles strong velocity heterogeneity and complex propagation paths. A successful RTM analysis with appropriate handling of boundary conditions results in enhanced signal-to-noise, accurately located structures, and minimal artifacts. A laser-ultrasound experiment begins with a source wave field generated at the surface that propagates through the sample. Acoustic scatterers in the propagation path give rise to a scattered wave field, which travels to the surface and is recorded by acoustic detectors. To reconstruct the laser-ultrasound image, a synthetic source function is forward propagated and cross-correlated with the time-reversed and back-propagated recorded (scattered) wave field to image the scatterers at the correct location. Conversely, photoacoustic waves are generated by chromophores within the sample and propagate "one-way" to the detection surface. We utilize the velocity model validated by the laser-ultrasound reconstruction to accurately reconstruct the photoacoustic image with RTM. This approach is first validated with simulations, where inclusions behave both as a photoacoustic source and an acoustic scatterer. Subsequently, we demonstrate the capabilities of RTM with tissue phantom experiments using an all-optical, multi-channel acquisition geometry.