Background Cardiac magnetic resonance imaging (CMR) is a powerful diagnostic modality that provides detailed quantitative assessment of cardiac anatomy and function. Automated extraction of CMR measurements from clinical reports that are typically stored as unstructured text in electronic health record systems would facilitate their use in research. Existing machine learning approaches either rely on large quantities of expert annotation or require the development of engineered rules that are time-consuming and are specific to the setting in which they were developed. Objective We hypothesize that the use of pretrained transformer-based language models may enable label-efficient numerical extraction from clinical text without the need for heuristics or large quantities of expert annotations. Here, we fine-tuned pretrained transformer-based language models on a small quantity of CMR annotations to extract 21 CMR measurements. We assessed the effect of clinical pretraining to reduce labeling needs and explored alternative representations of numerical inputs to improve performance. Methods Our study sample comprised 99,252 patients that received longitudinal cardiology care in a multi-institutional health care system. There were 12,720 available CMR reports from 9280 patients. We adapted PRAnCER (Platform Enabling Rapid Annotation for Clinical Entity Recognition), an annotation tool for clinical text, to collect annotations from a study clinician on 370 reports. We experimented with 5 different representations of numerical quantities and several model weight initializations. We evaluated extraction performance using macroaveraged F1-scores across the measurements of interest. We applied the best-performing model to extract measurements from the remaining CMR reports in the study sample and evaluated established associations between selected extracted measures with clinical outcomes to demonstrate validity. Results All combinations of weight initializations and numerical representations obtained excellent performance on the gold-standard test set, suggesting that transformer models fine-tuned on a small set of annotations can effectively extract numerical quantities. Our results further indicate that custom numerical representations did not appear to have a significant impact on extraction performance. The best-performing model achieved a macroaveraged F1-score of 0.957 across the evaluated CMR measurements (range 0.92 for the lowest-performing measure of left atrial anterior-posterior dimension to 1.0 for the highest-performing measures of left ventricular end systolic volume index and left ventricular end systolic diameter). Application of the best-performing model to the study cohort yielded 136,407 measurements from all available reports in the study sample. We observed expected associations between extracted left ventricular mass index, left ventricular ejection fraction, and right ventricular ejection fraction with clinical outcomes like atrial fibrillation, heart failure, and mortality. Conclusions This study demonstrated that a domain-agnostic pretrained transformer model is able to effectively extract quantitative clinical measurements from diagnostic reports with a relatively small number of gold-standard annotations. The proposed workflow may serve as a roadmap for other quantitative entity extraction.