Heat transfer in solids is typically conducted through either electrons or atomic vibrations known as phonons. In a vacuum, heat has long been thought to be transferred by radiation but not by phonons because of the lack of a medium(1). Recent theory, however, has predicted that quantum fluctuations of electromagnetic fields could induce phonon coupling across a vacuum and thereby facilitate heat transfer(2-4). Revealing this unique quantum effect experimentally would bring fundamental insights to quantum thermodynamics(5) and practical implications to thermal management in nanometre-scale technologies(6). Here we experimentally demonstrate heat transfer induced by quantum fluctuations between two objects separated by a vacuum gap. We use nanomechanical systems to realize strong phonon coupling through vacuum fluctuations, and observe the exchange of thermal energy between individual phonon modes. The experimental observation agrees well with our theoretical calculations and is unambiguously distinguished from other effects such as near-field radiation and electrostatic interaction. Our discovery of phonon transport through quantum fluctuations represents a previously unknown mechanism of heat transfer in addition to the conventional conduction, convection and radiation. It paves the way for the exploitation of quantum vacuum in energy transport at the nanoscale.