Faithful storage and coherent manipulation of quantum optical pulses are key for long distance quantum communications and quantum computing. Combining these functions in a light-matter interface that can be integrated on-chip with other photonic quantum technologies, e.g. sources of entangled photons, is an important step towards these applications. To date there have only been a few demonstrations of coherent pulse manipulation utilizing optical storage devices compatible with quantum states, and that only in atomic gas media (making integration difficult) and with limited capabilities. Here we describe how a broadband waveguide quantum memory based on the Atomic Frequency Comb (AFC) protocol can be used as a programmable processor for essentially arbitrary spectral and temporal manipulations of individual quantum optical pulses. Using weak coherent optical pulses at the few photon level, we experimentally demonstrate sequencing, time-to-frequency multiplexing and demultiplexing, splitting, interfering, temporal and spectral filtering, compressing and stretching as well as selective delaying. Our integrated light-matter interface offers high-rate, robust and easily configurable manipulation of quantum optical pulses and brings fully practical optical quantum devices one step closer to reality. Furthermore, as the AFC protocol is suitable for storage of intense light pulses, our processor may also find applications in classical communications.