The objective of the H₂ optimization of the dynamic vibration absorbers (DVAs) is to minimize the vibration energy transmitted to the system from the source of excitation. In this optimization criterion, the squared area (called H₂-norm) under the frequency response curve of the system is minimized. If the system is subjected to random excitation instead of sinusoidal one, then the H₂ optimization is probably desirable than the popular H_∞ optimization. The H₂ optimization is a classical optimization problem of DVAs, and has been already solved for a special case when the primary system has no damping. However, for the general case where the damping is present in the primary system, the H₂ optimization problem is not solved by algebraic approach until today. This paper proposes a closed-form exact solution for the H₂ optimization of DVAs attached to the damped primary systems.