In observational studies, confounder selection is a crucial task in estimation of causal effects of an exposure. For example, there are numerous potential confounding variables that we can take into account in research to measure the causal effect of air pollutant emissions on air quality (particulate matter) of interest. Several approaches have been proposed to estimate causal effects in the setting of high-dimensional potential confounders; however, many of them do not accommodate complex structures and interactions in the relationship to the outcome and exposure variables. In this work, we propose a Bayesian nonparametric approach to select confounders and estimate causal effects without assuming model structures for exposure and outcome variables. With the Bayesian additive regression trees (BART) method, the causal estimation model can flexibly capture complex data structure and select a subset of true confounders by specifying a common prior on the selection probabilities in both exposure and outcome models. The proposed model does not require a separate process to average effects across many models as, in our method, selection of confounders and estimation of causal effects based on the selected confounders are processed simultaneously within each MCMC iteration. A set of extensive simulation studies demonstrates that the proposed method performs well in many situations. The proposed model is used in an air pollution study to assess the causal effect of coal-emissions exposure to ambient PM2.5 concentrations in the presence of a large number of potential confounders.