Organisms use hair-like cilia that beat in a metachronal fashion to actively transport fluid and suspended particles. Metachronal motion emerges due to a phase difference between beating cycles of neighboring cilia and appears as traveling waves propagating along ciliary carpet. In this work, we demonstrate biomimetic artificial cilia capable of metachronal motion. The cilia are micromachined magnetic thin filaments attached at one end to a substrate and actuated by a uniform rotating magnetic field. We show that the difference in magnetic cilium length controls the phase of the beating motion. We use this property to induce metachronal waves within a ciliary array and explore the effect of operation parameters on the wave motion. The metachronal motion in our artificial system is shown to depend on the magnetic and elastic properties of the filaments, unlike natural cilia, where metachronal motion arises due to fluid coupling. Our approach enables an easy integration of metachronal magnetic cilia in lab-on-a-chip devices for enhanced fluid and particle manipulations.