An elementary quantum network operation involves storing a qubit state in an atomic quantum memory node, and then retrieving and transporting the information through a single photon excitation to a remote quantum memory node for further storage or analysis. Implementations of quantum network operations are thus conditioned on the ability to realize matter-to-light and/or light-to-matter quantum state mappings. Here we report the generation, transmission, storage and retrieval of single quanta using two remote atomic ensembles. A single photon is generated from a cold atomic ensemble at one site , and is directed to another site through 100 metres of optical fibre. The photon is then converted into a single collective atomic excitation using a dark-state polariton approach. After a programmable storage time, the atomic excitation is converted back into a single photon. This is demonstrated experimentally, for a storage time of 0.5 microseconds, by measurement of an anti-correlation parameter. Storage times exceeding ten microseconds are observed by intensity cross-correlation measurements. This storage period is two orders of magnitude longer than the time required to achieve conversion between photonic and atomic quanta. The controlled transfer of single quanta between remote quantum memories constitutes an important step towards distributed quantum networks.