Neutron scattering experiments on a polycrystalline sample of the frustrated pyrochlore magnet Tb2Ti2O7, which does not show any magnetic order down to 50 mK, have revealed that it shows condensation behavior below 0.4 K from a thermally fluctuating paramagnetic state to a spin-liquid ground-state with quantum spin fluctuations. Energy spectra change from quasielastic scattering to a continuum with a double-peak structure at energies of 0 and 0.8 K in the spin-liquid state. Specific heat shows an anomaly at the crossover temperature.