The olfactory system receives intermittent and fluctuating inputs arising from dispersion of odor plumes and active sampling by the animal. Previous work has suggested that the olfactory transduction machinery and excitatory-inhibitory olfactory bulb circuitry generate nonlinear population trajectories of neuronal activity that differ across odorants. Here we show that individual mitral/tufted (M/T) cells sum inputs linearly across odors and time. By decoupling odor sampling from respiration in anesthetized rats, we show that M/T cell responses to arbitrary odor waveforms and mixtures are well described by odor-specific impulse responses convolved with the odorant's temporal profile. The same impulse responses convolved with the respiratory airflow predict the classical respiration-locked firing of olfactory bulb neurons and several other reported response properties of M/T cells. These results show that the olfactory bulb linearly processes fluctuating odor inputs, thereby simplifying downstream decoding of stimulus identity and temporal dynamics.