Recent advances in producing samples of molecules at very low temperatures have been motivated by the prospects of studying collisions and chemical reactions with controllable collision energies, performing high resolution spectroscopy and precision measurements for fundamental physics, quantum information processing and quantum simulation. Methods based on the deceleration of supersonic molecular beams are particularly well suited for collision experiments since the final longitudinal velocity of the sample can be tuned over a wide range with narrow velocity spreads. Zeeman deceleration methods rely on the state-dependent interaction of neutral paramagnetic atoms or molecules with a time-dependent inhomogeneous magnetic fields. For this reason, the Zeeman deceleration technique is especially effective in open-shell systems such as molecular radicals or metastable atoms and molecules. Here, an experimental realization of a novel travelling-wave Zeeman decelerator based on a double-helix wire geometry is presented. The decelerator is capable of decelerating samples of paramagnetic atoms and molecules from 560 m/s forward velocity down to an arbitrary final velocity. Compared to the conventional Zeeman or Stark decelerators, the presented decelerator exhibits full three-dimensional confinement of the molecules at a full range of velocities starting from the initial forward velocity down to the arbitrary final velocity, leading to an improvement of the overall phase-space acceptance compared to the conventional Zeeman and Stark decelerators. Operation of the decelerator is demonstrated by deceleration of a molecular beam of OH radicals from an initial velocity of 445 m/s down to a final velocity of 350 m/s. The experimental results are accompanied by numerical trajectory simulations confirming stable operation and showing phase-space stability of the decelerator. These results pave the way for the future cold-collision experiments. In the future, the traveling-wave Zeeman decelerator will serve as a source of cold paramagnetic molecules for hybrid trapping experiments.