Geological storage of CO2 in saline aquifers and depleted oil and gas reservoirs can help mitigate CO2 emissions. However, CO2 leakage over a long storage period represents a potential concern. Therefore, it is critical to establish a good understanding of the interactions between CO2–brine and cement–caprock/reservoir rock to ascertain the potential for CO2 leakage. Accordingly, in this work, we prepared a unique set of composite samples to resemble the cement–reservoir rock interface. A series of experiments simulating deep wellbore environments were performed to investigate changes in chemical, physical, mechanical, and petrophysical properties of the composite samples. Here, we present the characterisation of composite core samples, including porosity, permeability, and mechanical properties, determined before and after long-term exposure to CO2-rich brine. Some of the composite samples were further analysed by X-ray microcomputed tomography (X-ray µ-CT), X-ray diffraction (XRD), and scanning electron microscopy–energy-dispersive X-ray (SEM–EDX). Moreover, the variation of ions concentration in brine at different timescales was studied by performing inductively coupled plasma (ICP) analysis. Although no significant changes were observed in the porosity, permeability of the treated composite samples increased by an order of magnitude, due mainly to an increase in the permeability of the sandstone component of the composite samples, rather than the cement or the cement/sandstone interface. Mechanical properties, including Young’s modulus and Poisson’s ratio, were also reduced.