A fundamental challenge in soft matter physics is to describe materials, such as the living cytoplasm and tissues, that are simultaneously active, chemically driven, and exhibit long-lasting memory of mechanical stresses. Here, we construct a generalized hydrodynamic framework at finite wavevectors and frequencies that is applicable to non-equilibrium fluids with memory. By leveraging stationary correlation identities, we derive a generalized linear response theory for non-equilibrium steady states. This framework serves as a formal extension of Onsager’s regression hypothesis beyond thermal equilibrium. Our approach provides a direct pathway to derive transport coefficients from steady-state fluctuations without the traditional Mori–Zwanzig projection-operator formalism, generalizing the Green–Kubo relations to non-equilibrium systems. As a corollary, we derive two model-free variants of the non-equilibrium fluctuation-response relation for non-Markovian dynamics. These generalized relations explicitly capture the non-equilibrium circulating currents—an out-of-equilibrium signature that is invisible to conventional scalar formulations or frameworks that treat degrees of freedom independently. Applying our theory to chemically driven active fluids reveals the emergence of active viscoelastic memory, wherein chemical reaction cycles dynamically renormalize the macroscopic viscous response. Strikingly, this active memory can induce negative storage modulus at finite frequencies, a behavior absent in ordinary viscoelastic fluids. Our first-principles framework rigorously extends linear rheology to non-equilibrium systems and provides a foundation for understanding non-Markovian dynamics across a broad range of biological and synthetic active matter.