In this paper, a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery is introduced. Following the linear mixing model, each pixel spectrum of the hyperspectral image is decomposed as a linear combination of pure endmember spectra. The estimation of the unknown endmember spectra and the corresponding abundances is conducted in a unified manner by generating the posterior distribution of the unknown parameters under a hierarchical Bayesian model. The proposed model accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember spectra lie on a lower dimensional space. A Gibbs algorithm is proposed to generate samples distributed according to the posterior of interest. Simulation results illustrate the accuracy of the proposed joint Bayesian estimator.