Introduction: The amygdala is known to play a role in mediating emotion and possibly addiction. We used probabilistic tractography (PT) to evaluate whether structural connectivity of the amygdala to the brain reward network is associated with impulsive choice and tobacco smoking. Methods: Diffusion and structural MRI scans were obtained from 197 healthy subjects (45 with a history of tobacco smoking) randomly sampled from the Human Connectome database. PT was performed to assess amygdala connectivity with several brain regions. Seed masks were generated, and statistical maps of amygdala connectivity were derived. Connectivity results were correlated with a subject performance both on a delayed discounting task and whether they met specified criteria for difficulty quitting smoking. Results: Amygdala connectivity was spatially segregated, with the strongest connectivity to the hippocampus, orbitofrontal cortex (OFC), and brainstem. Connectivity with the hippocampus was associated with preference for larger delayed rewards, whereas connectivity with the OFC, rostral anterior cingulate cortex (rACC), and insula were associated with preference for smaller immediate rewards. Greater nicotine dependence with difficulty quitting was associated with less hippocampal and greater brainstem connectivity. Scores on the Fagerstrom Test for Nicotine Dependence (FTND) correlated with rACC connectivity. Discussion: These findings highlight the importance of the amygdala-hippocampal-ACC network in the valuation of future rewards and substance dependence. These results will help to identify potential targets for neuromodulatory therapies for addiction and related disorders.