Parameters of the solar cell equivalent circuit models have a significant role in assessing the solar cells’ performance and tracking operational variations. In this regard, estimating solar cell parameters is a difficult task because cells have nonlinear current-voltage characteristics. Thus, a fast and accurate optimization algorithm is usually required to solve this engineering problem effectively. This paper proposes two hybrid variants of honey badger algorithm (HBA) and artificial gorilla troops optimizer (GTO) to estimate solar cell parameters. The proposed algorithms minimize the root mean square error (RMSE) between measurement and simulation results. In the first variant, GTO is used to determine the initial population of HBA, while in the second variant, HBA is used to determine the initial population of GTO. These variants can efficiently improve convergence characteristics. The proposed optimization algorithms are applied for parameter estimation of different equivalent circuit models of solar cells and various photovoltaic (PV) modules. Namely, the proposed algorithms test three solar cell equivalent models: single-diode, double-diode, and triple-diode equivalent circuit models. Different photovoltaic modules are investigated, such as the RadioTechnique Compelec (RTC) France solar cell, Solarex’s Multicrystalline 60 watts solar module (MSX 60), and the Photowatt, France solar panel (Photo-watt PWP 201). In addition, the applicability of the proposed optimization algorithms is verified using obtained results from a commercial solar module called Shell Monocrystalline PV module (SM55) with different irradiation and temperature levels. The good results of the proposed algorithms show that they can efficiently improve convergence speed and the accuracy of the obtained results than other algorithms used for parameter estimation of PV equivalent circuit models in the literature, particularly in terms of the values of the RMSE and statistical tests. In addition, the parameters estimated by the proposed methods fit the simulation data perfectly at different irradiance and temperature levels for the commercial PV module.