The damped outrigger system is in widespread use as a damping modification system for tall buildings that provides high additional damping in addition to the bending back effect against the core. However, while the enhanced seismic performance of damped outrigger systems was confirmed in previous studies all over the world, a general-purpose optimal design method focusing on modal damping ratios has not been established yet. This paper proposes an optimal damper design kit composed of a first mode damping ratio oriented design policy, simple equations of optimal damper-connection stiffness ratio to maximize first mode damping ratio, a machine learning model to estimate first mode natural period and damping ratio. The tenability of the first mode damping ratio-oriented design policy was confirmed by performing complex modal analyses on single to quad damped outrigger systems incorporating linear viscous dampers and assigning realistic stiffness values to the outrigger trusses. The simple design equations of optimal damper-connection stiffness ratio and the machine learning model for first mode characteristics were developed based on a large number of analytical results. The proposed optimal design kit has been made available as a web application-based design tool.