The degradation of cellulose-based fibrous networks is due to complex physical and chemical processes that occur as the material ages and are enhanced by environmental factors (e.g., temperature and relative humidity) and intrinsic parameters (e.g., the acidity of the material). This contribution presents a novel computational model to predict the degradation and lifetime of cellulose-based fibrous networks, which may be applied to degradation studies on historical paper. The approach is based on i) a multi-physics modeling framework, which considers the relevant chemical and mechanical degradation processes and the influence of the ambient environmental conditions, and ii) a multi-scale description, which includes fiber- and fibrous network effects into the effective macro-scale response. The cellulose fibers composing the fibrous network are characterized by an age-dependent, chemo-mechanical constitutive behavior. An evolution equation describes the reduction of the degree of polymerization of cellulose as a function of time and the specific environmental conditions, which in turn is used for determining the fiber tensile strength. The fiber stresses induced by hygro-expansion and hygro-contraction under a change in relative humidity are computed using a coupled hygro-mechanical model and lead to brittle damage once the fiber tensile strength is reached. Accordingly, the chemical degradation of individual fibers affects the local damage development and stress distribution in the fibrous network, thereby governing the material response at the macroscopic scale. Asymptotic homogenization applies to calculate the effective hygro-mechanical properties of the fibrous network. A set of numerical simulations predicts the time-dependent degradation of cellulose-based fibrous networks under a range of temperature, relative humidity, and acidity conditions.