Bioimpedance modeling with equivalent electrical circuits has an important role in various biomedical applications, as it facilitates understanding of underlying physical and electrochemical processes in applications such as body composition measurements and assessment of clinical conditions. However, the estimation of model parameter values is not a straightforward task, especially when complex circuits with fractional-order components [e.g., constant phase elements (CPEs)] are used. In this article, we propose a low-complexity method for parameter estimation of the Cole-impedance model suitable for low-cost embedded hardware (e.g., 8-bit microcontrollers). Our approach uses only the measured real and imaginary impedance, without any specific software package/toolbox, or initial values provided by the user. The proposed method was validated with synthetic (noiseless and noisy) data and experimental right-side, hand-to-foot bioimpedance data from a healthy adult participant. Moreover, the proposed method was compared in terms of accuracy with the recently published relevant work and commercial Electrical Impedance Spectroscopy software (Bioimp 2.3.4). The performance evaluation in terms of complexity (suitable for deployment for the microcontroller-based platform with 256 kB of RAM and 16 MHz clock speed), execution time (18 s for the dataset with 256 points), and cost (< 25) confirms the proposed method in regards to reliable bioimpedance processing using embedded hardware.