In this work, we first perform a systematic search for high-efficiency three-dimensional (3D) and two-dimensional (2D) thermoelectric materials by combining semiclassical transport techniques with density functional theory (DFT) calculations and then train machine-learning models on the thermoelectric data. Out of 36000 three-dimensional and 900 two-dimensional materials currently in the publicly available JARVIS-DFT database, we identify 2932 3D and 148 2D promising thermoelectric materials using a multi-steps screening procedure, where specific thresholds are chosen for key quantities like bandgaps, Seebeck coefficients and power factors. We compute the Seebeck coefficients for all the materials currently in the database and validate our calculations by comparing our results, for a subset of materials, to experimental and existing computational datasets. We also investigate the effect of chemical, structural, crystallographic and dimensionality trends on thermoelectric performance. We predict several classes of efficient 3D and 2D materials such as Ba(MgX)2 (X=P,As,Bi), X2YZ6 (X=K,Rb, Y=Pd,Pt, Z=Cl,Br), K2PtX2(X=S,Se), NbCu3X4 (X=S,Se,Te), Sr2XYO6 (X=Ta, Zn, Y=Ga, Mo), TaCu3X4 (X=S, Se,Te), and XYN (X=Ti, Zr, Y=Cl, Br). Finally, as high-throughput DFT is computationally expensive, we train machine learning models using gradient boosting decision trees (GBDT) and classical force-field inspired descriptors (CFID) for n-and p-type Seebeck coefficients and power factors, to quickly pre-screen materials for guiding the next set of DFT calculations. The dataset and tools are made publicly available at the websites: https://www.ctcms.nist.gov/~knc6/JVASP.html , https://www.ctcms.nist.gov/jarvisml/ and https://jarvis.nist.gov/ .