Continuous monitoring of engineering structures provides a crucial alternative to assess its health condition as well as evaluate its safety throughout the whole service life. To link the field measurements to the characteristics of a building, one option is to characterize and update a model, against the measured data, so that it can best describe the behavior and performance of the structure. In this paper, we present a novel computational strategy for Bayesian probabilistic updating of building models with response functions extracted from ambient noise measurements using seismic interferometry. The intrinsic building impulse response functions (IRFs) can be extracted from ambient excitation by deconvolving the motion recorded at different floors with respect to the measured ambient ground motion. The IRF represents the representative building response to an input delta function at the ground floor. The measurements are firstly divided into multiple windows for deconvolution and the IRFs for each window are then averaged to represent the overall building IRFs. A hierarchical Bayesian framework with Laplace priors is proposed for updating the finite element model. A Markov chain Monte Carlo technique with adaptive random-walk steps is employed to sample the model parameters for uncertainty quantification. An illustrative example is studied to validate the effectiveness of the proposed algorithm for temporal monitoring and probabilistic model updating of buildings. The structure considered in this paper is a 21-storey concrete building instrumented with 36 accelerometers at the MIT campus. The methodology described here allows for continuous temporal health monitoring, robust model updating as well as post-earthquake damage detection of buildings.