In this work, we propose a new Bayesian spatially clustered coefficient (BSCC) regression model, to detect spatial clustering patterns in the associations between response variables and covariates. In BSCC, regression coefficients are assumed to be constants within each spatially contiguous cluster. To model the clustering patterns, we develop a novel and flexible space partitioning prior based on Euclidean spanning trees, which is capable of capturing irregularly shaped clusters. An efficient Reversible Jump Markov chain Monte Carlo (MCMC) algorithm is designed to estimate the clustered coefficient values and their uncertainty measures. Finally, we illustrate the performance of the model with simulation studies and a real data analysis of temperature-salinity relationship in the Atlantic Ocean.