We report on the measurement of freeze-out radii for pairs of identical-charge pions measured in Pb-Pb collisions at sNN=2.76 TeV as a function of collision centrality and the average transverse momentum of the pair kT. Three-dimensional sizes of the system (femtoscopic radii), as well as direction-averaged one-dimensional radii are extracted. The radii decrease with kT, following a power-law behavior. This is qualitatively consistent with expectations from a collectively expanding system, produced in hydrodynamic calculations. The radii also scale linearly with (dNch/dη)1/3. This behavior is compared to world data on femtoscopic radii in heavy-ion collisions. While the dependence is qualitatively similar to results at smaller sNN, a decrease in the ratio Rout/Rside is seen, which is in qualitative agreement with a specific prediction from hydrodynamic models: a change from inside-out to outside-in freeze-out configuration. The results provide further evidence for the production of a collective, strongly coupled system in heavy-ion collisions at the CERN Large Hadron Collider. © 2016 CERN.