The next generation of civil large aero-engines will employ greater bypass ratios compared with contemporary architectures. This results in higher exchange rates between exhaust performance and specific fuel consumption (SFC). Concurrently, the aerodynamic design of the exhaust is expected to play a key role in the success of future turbofans. This paper presents the development of a computational framework for the aerodynamic design of separate-jet exhaust systems for civil aero-engines. A mathematical approach is synthesised based on class-shape transformation (CST) functions for the parametric geometry definition of gas-turbine exhaust components such as annular ducts and nozzles. This geometry formulation is coupled with an automated viscous and compressible flow solution method and a cost-effective design space exploration (DSE) approach. The framework is deployed to optimise the performance of a separate-jet exhaust for very-high-bypass ratio (VHBR) turbofan engine. The optimisations carried out suggest the potential to increase the engine’s net propulsive force compared with a baseline architecture, through optimum exhaust re-design. The proposed method is able to identify and alleviate adverse flow-features that may deteriorate the aerodynamic behaviour of the exhaust system.