Quantum teleportation is central to the practical realization of quantum communication. Although the first proof-of-principle demonstration was reported in 1997 by the Innsbruck and Rome groups, long-distance teleportation has so far only been realized in fibre with lengths of hundreds of metres. An optical free-space link is highly desirable for extending the transfer distance, because of its low atmospheric absorption for certain ranges of wavelength. By following the Rome scheme, which allows a full Bell-state measurement, we report free-space implementation of quantum teleportation over 16km. An active feed-forward technique has been developed to enable real-time information transfer. An average fidelity of 89%, well beyond the classical limit of 2/3, is achieved. Our experiment has realized all of the non-local aspects of the original teleportation scheme and is equivalent to it up to a local unitary operation. Our result confirms the feasibility of space-based experiments, and is an important step towards quantum-communication applications on a global scale.