Interactions between the brain and body are of fundamental importance for human behavior and health. Functional magnetic resonance imaging (fMRI) captures whole-brain activity noninvasively, and modeling how fMRI signals interact with physiological dynamics of the body can provide new insight into brain function and offer potential biomarkers of disease. However, physiological recordings are not always possible to acquire since they require extra equipment and setup, and even when they are, the recorded physiological signals may contain substantial artifacts. To overcome this limitation, machine learning models have been proposed to directly extract features of respiratory and cardiac activity from resting-state fMRI signals. To date, such work has been carried out only in healthy young adults and in a pediatric population, leaving open questions about the efficacy of these approaches on older adults. Here, we propose a novel framework that leverages Transformer-based architectures for reconstructing two key physiological signals - low-frequency respiratory volume (RV) and heart rate (HR) fluctuations - from fMRI data, and test these models on a dataset of individuals aged 36-89 years old. Our framework outperforms previously proposed approaches (attaining median correlations between predicted and measured signals of r ~ .698 for RV and r ~ .618 for HR), indicating the potential of leveraging attention mechanisms to model fMRI-physiological signal relationships. We also evaluate several model training and fine-tuning strategies, and find that incorporating young-adult data during training improves the performance when predicting physiological signals in the aging cohort. Overall, our approach successfully infers key physiological variables directly from fMRI data from individuals across a wide range of the adult lifespan.