The cogeneration system described in this paper is constructed based on a solar-assisted double-effect absorption cogeneration cycle with an adjustable cooling-to-power ratio. As a proposed technique to benefit from the ability to adjust the cooling-to-power ratio, this system is integrated with a cold thermal energy storage system. The procedure described here will be applied to a combined cooling and power system with a thermal energy storage capability for a large medical center in Jeddah, Saudi Arabia. Through an exergoeconomic analysis of the integrated system on a typical summer day in Jeddah, we found that the integrated system could fulfill the cooling and power demands of the medical center under study with an exergetic efficiency of 53.97%. From an economics perspective, the integrated system was found to deliver cooling and power with average unit costs of 222.89 $/GJ and 17.06 $/GJ, respectively. These costs were found to be lower than the unit costs of the respective cooling and power costs delivered to the medical center if they were obtained from an electrically-driven vapor compression system and the electric grid, respectively. For the case study investigated, it has been found that using the integrated system is a desirable approach due to the system’s lower unit costs as well as its relatively short payback period. Additionally, it has been found that although cogeneration systems constructed based on the double-effect combined cooling and power cycle have higher exergy destruction and capital investment rates, they have a lower unit cost for the produced exergy in comparison with those of cogeneration systems constructed based on a single-effect combined cooling and power cycle.