Digital breast tomosynthesis (DBT) has gained popularity as breast imaging modality due to its pseudo-3D reconstruction and improved accuracy compared to digital mammography. However, DBT faces challenges in image quality and quantitative accuracy due to scatter radiation. Recent advancements in deep learning (DL) have shown promise in using fast convolutional neural networks for scatter correction, achieving comparable results to Monte Carlo (MC) simulations. To predict the scatter radiation signal in DBT projections within clinically-acceptable times and using only clinically-available data, such as compressed breast thickness and acquisition angle. MC simulations to obtain scatter estimates were generated from two types of digital breast phantoms. One set consisted of 600 realistically-shaped homogeneous breast phantoms for initial DL training. The other set was composed of 80 anthropomorphic phantoms, containing realistic internal tissue texture, aimed at fine tuning the DL model for clinical applications. The MC simulations generated scatter and primary maps per projection angle for a wide-angle DBT system. Both datasets were used to train (using 7680 projections from homogeneous phantoms), validate (using 960 and 192 projections from the homogeneous and anthropomorphic phantoms, respectively), and test (using 960 and 48 projections from the homogeneous and anthropomorphic phantoms, respectively) the DL model. The DL output was compared to the corresponding MC ground truth using both quantitative and qualitative metrics, such as mean relative and mean absolute relative differences (MRD and MARD), and to previously-published scatter-to-primary (SPR) ratios for similar breast phantoms. The scatter corrected DBT reconstructions were evaluated by analyzing the obtained linear attenuation values and by visual assessment of corrected projections in a clinical dataset. The time required for training and prediction per projection, as well as the time it takes to produce scatter-corrected projection images, were also tracked. The quantitative comparison between DL scatter predictions and MC simulations showed a median MRD of 0.05% (interquartile range (IQR), -0.04% to 0.13%) and a median MARD of 1.32% (IQR, 0.98% to 1.85%) for homogeneous phantom projections and a median MRD of -0.21% (IQR, -0.35% to -0.07%) and a median MARD of 1.43% (IQR, 1.32% to 1.66%) for the anthropomorphic phantoms. The SPRs for different breast thicknesses and at different projection angles were within±15% of the previously-published ranges. The visual assessment showed good prediction capabilities of the DL model with a close match between MC and DL scatter estimates, as well as between DL-based scatter corrected and anti-scatter grid corrected cases. The scatter correction improved the accuracy of the reconstructed linear attenuation of adipose tissue, reducing the error from -16% and -11% to -2.3% and 4.4% for an anthropomorphic digital phantom and clinical case with similar breast thickness, respectively. The DL model training took 40 min and prediction of a single projection took less than 0.01s. Generating scatter corrected images took 0.03s per projection for clinical exams and 0.16s for one entire projection set. This DL-based method for estimating the scatter signal in DBT projections is fast and accurate, paving the way for future quantitative applications.