We study how well the mass of the graviton can be constrained from gravitational-wave ( GW ) observations of coalescing binary black holes . Whereas the previous investigations employed post-Newtonian ( PN ) templates describing only the inspiral part of the signal , the recent progress in analytical and numerical relativity has provided analytical waveform templates coherently describing the inspiral-merger-ringdown ( IMR ) signals . We show that a search for binary black holes employing IMR templates will be able to constrain the mass of the graviton much more accurately ( \sim an order of magnitude ) than a search employing PN templates . The best expected bound from GW observatories ( \lambda _ { g } > 7.8 \times 10 ^ { 13 } km from Adv . LIGO , \lambda _ { g } > 7.1 \times 10 ^ { 14 } km from Einstein Telescope , and \lambda _ { g } > 5.9 \times 10 ^ { 17 } km from LISA ) are several orders-of-magnitude better than the best available model-independent bound ( \lambda _ { g } > 2.8 \times 10 ^ { 12 } km , from Solar system tests ) .