Rate of penetration (ROP) is crucial for evaluating drilling efficiency, with accurate prediction essential for enhancing performance and optimizing parameters. In practice, complex and variable downhole environments pose significant challenges for mechanistic ROP equations, resulting in prediction difficulties and low accuracy. Recently, data-driven machine learning models have been widely applied to ROP prediction. However, these models often lack mechanistic constraints, limiting their performance to specific conditions and reducing their real-world applicability. Additionally, geological variability across wells further hinders the transferability of conventional intelligent models. Thus, combining mechanistic knowledge with intelligent models and enhancing model stability and transferability are key challenges in ROP prediction research. To address these challenges, this paper proposes a Mechanism-Data Fusion and Transfer Learning method to construct an intelligent prediction model for ROP, achieving accurate ROP predictions. A multilayer perceptron (MLP) was selected as the base model, and training was performed using data from neighboring wells and partial data from the target well. The Two-stage TrAdaBoost.R2 algorithm was employed to enhance model transferability. Additionally, drilling mechanistic knowledge was incorporated into the model’s loss function as a constraint to achieve a fusion of mechanistic knowledge and data-driven approaches. Using MAPE as the measure of accuracy, compared with conventional intelligent models, the proposed ROP prediction model improved prediction accuracy on the target well by 64.51%. The model transfer method proposed in this paper has a field test accuracy of 89.71% in an oilfield in China. These results demonstrate the effectiveness and feasibility of the proposed transfer learning method and mechanistic–data integration approach.