© 2020, The Author(s), under exclusive licence to Springer Nature Limited. Models of light–matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a ‘giant atom’2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4–10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom–waveguide couplings with large on–off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide—an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit–qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13.