This paper presents a new parameters estimation method for the single diode model and the double diode model of photovoltaic cells. A new application of the slime mould algorithm (SMA) stochastic optimization method represents one of the main contributions in this paper. The employment of the slime mould algorithm provides highly accurate and fast determination procedures of photovoltaic cells parameters. The slime mould algorithm stochastic optimization provides unique mathematical modelling of the optimization problem through using adaptive weights. These adaptive weights emulate the process of generating positive and negative feedbacks in the propagated wave of the slime mould. Moreover, the slime mould algorithm is successful at accurately extracting the global optimal values for the solar photovoltaic cell parameters. It has the ability to handle the non-linearity and multi-modal properties of the photovoltaic cell characteristics. The proposed method provides a generalized solution for precisely determining the parameters for various photovoltaic cells technologies. Comprehensive comparisons of the proposed slime mould algorithm with existing photovoltaic cell parameter extraction methods are performed in the paper. The results confirm the superior performance and accuracy of the proposed slime mould algorithm over the existing methods.