We estimate the stochastic gravitational wave (GW) background signal from the field population of coalescing binary stellar mass black holes (BHs) throughout the universe. This study is motivated by recent observations of BH-Wolf-Rayet (WR) star systems and by new estimates in the metallicity abundances of star-forming galaxies that imply BH-BH systems are more common than previously assumed. Using recent analytical results of the inspiral-merger-ringdown waveforms for coalescing binary BH systems, we estimate the resulting stochastic GW background signal. Assuming average quantities for the single source energy emissions, we explore the parameter space of chirp mass and local rate density required for detection by advanced and third-generation interferometric GW detectors. For an average chirp mass of 8.7 M , we find that detection through 3 years of cross-correlation by two advanced detectors will require a rate density, r 0 >= 0.5 Mpc--3 Myr--1. Combining data from multiple pairs of detectors can reduce this limit by up to 40%. Investigating the full parameter space we find that detection could be achieved at rates r 0 ~ 0.1 Mpc--3 Myr--1 for populations of coalescing binary BH systems with average chirp masses of ~15 M which are predicted by recent studies of BH-WR star systems. While this scenario is at the high end of theoretical estimates, cross-correlation of data by two Einstein Telescopes could detect this signal under the condition r 0 >= 10--3Mpc--3 Myr--1. Such a signal could potentially mask a primordial GW background signal of dimensionless energy density, Delta *WGW ~ 10--10, around the (1-500) Hz frequency range.