Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance(1). Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons(2-5), ions(6) and electron spins(7), and more recently in microwave and electromechanical devices(8-10). For macroscopic-scale objects(8-14), however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 10(12) atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion(15-17). We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.