The production of K∗(892)0 and ϕ(1020) mesons in proton-proton (pp) and lead-lead (Pb-Pb) collisions at √sNN=2.76TeV has been analyzed using a high luminosity data sample accumulated in 2011 with the ALICE detector at the Large Hadron Collider (LHC). Transverse momentum (pT) spectra have been measured for K∗(892)0 and ϕ(1020) mesons via their hadronic decay channels for pT up to 20GeV/c. The measurements in pp collisions have been compared to model calculations and used to determine the nuclear modification factor and particle ratios. The K∗(892)0/K ratio exhibits significant reduction from pp to central Pb-Pb collisions, consistent with the suppression of the K∗(892)0 yield at low pT due to rescattering of its decay products in the hadronic phase. In central Pb-Pb collisions the pT dependent ϕ(1020)/π and K∗(892)0/π ratios show an enhancement over pp collisions for pT≈3GeV/c, consistent with previous observations of strong radial flow. At high pT, particle ratios in Pb-Pb collisions are similar to those meas