Diffusion tensor imaging (DTI) holds significant importance in clinical diagnosis and neuroscience research. However, conventional model-based fitting methods often suffer from sensitivity to noise, leading to decreased accuracy in estimating DTI parameters. While traditional data-driven deep learning methods have shown potential in terms of accuracy and efficiency, their limited generalization to out-of-training-distribution data impedes their broader application due to the diverse scan protocols used across centers, scanners, and studies. This work aims to tackle these challenges and promote the use of DTI by introducing a data-driven optimization-based method termed DoDTI. DoDTI combines the weighted linear least squares fitting algorithm and regularization by denoising technique. The former fits DW images from diverse acquisition settings into diffusion tensor field, while the latter applies a deep learning-based denoiser to regularize the diffusion tensor field instead of the DW images, which is free from the limitation of fixed-channel assignment of the network. The optimization object is solved using the alternating direction method of multipliers and then unrolled to construct a deep neural network, leveraging a data-driven strategy to learn network parameters. Extensive validation experiments are conducted utilizing both internally simulated datasets and externally obtained in-vivo datasets. The results, encompassing both qualitative and quantitative analyses, showcase that the proposed method attains state-of-the-art performance in DTI parameter estimation. Notably, it demonstrates superior generalization, accuracy, and efficiency, rendering it highly reliable for widespread application in the field.