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The purpose of the current study was to introduce a Deep learning-based Accelerated and Noise-Suppressed Estimation (DANSE) method for reconstructing quantitative maps of biological tissue cellular-specific, R2t*, and hemodynamic-specific, R2', metrics of quantitative gradient-recalled echo (qGRE) MRI. The DANSE method adapts a supervised learning paradigm to train a convolutional neural network for robust estimation of R2t* and R2' maps with significantly reduced sensitivity to noise and the adverse effects of macroscopic (B 0 ) magnetic field inhomogeneities directly from the gradient-recalled echo (GRE) magnitude images. The R2t* and R2' maps for training were generated by means of a voxel-by-voxel fitting of a previously developed biophysical quantitative qGRE model accounting for tissue, hemodynamic, and B 0 -inhomogeneities contributions to multigradient-echo GRE signal using a nonlinear least squares (NLLS) algorithm. We show that the DANSE model efficiently estimates the aforementioned qGRE maps and preserves all the features of the NLLS approach with significant improvements including noise suppression and computation speed (from many hours to seconds). The noise-suppression feature of DANSE is especially prominent for data with low signal-to-noise ratio (SNR ~ 50-100), where DANSE-generated R2t* and R2' maps had up to three times smaller errors than that of the NLLS method. The DANSE method enables fast reconstruction of qGRE maps with significantly reduced sensitivity to noise and magnetic field inhomogeneities. The DANSE method does not require any information about field inhomogeneities during application. It exploits spatial and gradient echo time-dependent patterns in the GRE data and previously gained knowledge from the biophysical model, thus producing high quality qGRE maps, even in environments with high noise levels. These features along with fast computational speed can lead to broad qGRE clinical and research applications., (© 2022 John Wiley & Sons Ltd.)