Numerous materials feature unexplained phases with invisible or hidden order of electronic origin. A particularly mysterious case is that of Tb₂Ti₂O₇, which avoids magnetic order to the lowest temperatures, but nevertheless has an unexplained second-order phase transition near T=0.5 K. Our ultrasound measurements of Tb₂Ti₂O₇ provide direct evidence of a huge softening followed by strong hardening of the structural lattice below T = 0.5 K. In the absence of magnetic order at this temperature, our results provide conclusive evidence for the proposed quadrupolar order and emphasize the importance of higher-order multipolar interactions in rare-earth frustrated magnets.