Thyroid cancer is the most common malignant endocrine tumor. The key test to assess preoperative risk of malignancy is cytologic evaluation of fine-needle aspiration biopsies (FNABs). The evaluation findings can often be indeterminate, leading to unnecessary surgery for benign post-surgical diagnoses. We have developed a deep-learning algorithm to analyze thyroid FNAB whole-slide images (WSIs). We show, on the largest reported data set of thyroid FNAB WSIs, clinical-grade performance in the screening of determinate cases and indications for its use as an ancillary test to disambiguate indeterminate cases. The algorithm screened and definitively classified 45.1% (130/288) of the WSIs as either benign or malignant with risk of malignancy rates of 2.7% and 94.7%, respectively. It reduced the number of indeterminate cases (N = 108) by reclassifying 21.3% (N = 23) as benign with a resultant risk of malignancy rate of 1.8%. Similar results were reproduced using a data set of consecutive FNABs collected during an entire calendar year, achieving clinically acceptable margins of error for thyroid FNAB classification.