Designing detection systems based on transimpedance amplifiers is a complex task because noise, frequency response, and stability are coupled constraints. This work presents a straightforward design method of detection systems based on transimpedance amplifiers. We take into account the objectives, scope of the design, and requirements and specifications, including the input signal levels. According to the small-signal model, the noise and stability are analyzed in detail. We present a systematic procedure to search for the acceptable values of the feedback network components based on these analyses. Then, we define a merit function to compare the performance of the acceptable combinations of feedback network components. For every acceptable combination, the function gives a quantitative measure of the degree of compliance for each design parameter: signal-to-noise ratio, highest operating frequency, and phase margin. As an example, we apply the method to optimize the design of an optical detection system using a PIN photodiode and a low-noise operational amplifier.