This paper aims to develop a general form of the time-temperature-ageing shift model for bituminous materials based on free volume theory and validate its application in the Finite Element (FE) modelling for predicting aged asphalt mixtures’ mechanical responses. The frequency sweep, dynamic modulus, and Fourier Transform Infrared Spectroscopy (FTIR) tests were used to validate the proposed time-temperature-ageing shift model. A generalised Maxwell model incorporating the proposed shift model of asphalt mixtures was used to predict the mechanical responses of aged asphalt mixtures using FE modelling, verified via laboratory cyclic load tests. Results indicate that the time-temperature-ageing shift function can model the complex shear modulus and dynamic modulus master curves of bituminous materials, addressing the modulus dependency of temperature and ageing. Temperature dominates the modulus change of bituminous materials in the ageing process. The coefficients of the time-temperature-ageing shift model have clear physical meanings and can potentially quantify the effects of asphalt mixtures’ air voids on their temperature and ageing susceptibilities. The time-temperature-ageing shift model can be incorporated into the constitutive relations of the FE model to effectively couple and efficiently predict the effects of temperature and ageing on the mechanical responses of aged asphalt mixtures.