In this work, a novel solar double-effect absorption combined cooling and power (DECCP) system with an adjustable cooling-to-power ratio is proposed. This cogeneration system uses water–LiBr as the working fluid. The novel cycle upon which this system is based has been mathematically modeled, simulated, and parametrically analyzed to generate the system’s performance characteristics for several scenarios. The performance has been compared with those of other similar combined cogeneration cycles. It was found that the proposed cycle outperforms the other cycles from the vantage point of the power produced and the cycle’s ability to produce cooling. For specific operating parameters, the DECCP cycle achieves an exergetic efficiency that varies between 36.55% and 59.13% based on the refrigerant split ratio used. An effective operating strategy is proposed for the cycle when it is powered by solar energy.