We present results of Lagrangian troposphere-to-stratosphere transport (TST) in the tropics based on trajectory calculations for the period 1979--2001. The trajectories and corresponding temperature histories are calculated from wind and temperature fields provided by the reanalysis data ERA-40 of the European Centre for Medium-Range Weather Forecasts (ECMWF). The water vapor mixing ratio of air entering the tropical stratosphere is calculated from the minimum saturation mixing ratio over ice encountered by each trajectory. We show that this Lagrangian approach, which considers the global-scale to synoptic-scale dynamics of tropical TST but neglects mesoscale dynamics and details of cloud microphysics, substantially improves estimates of stratospheric humidity compared to calculations based on Eulerian mean tropical tropopause temperatures. For the period 1979--2001 we estimate from the Lagrangian calculation that the mean water mixing ratio of air entering the stratosphere is 3.5 ppmv, which is in good agreement with measurements during the same period, ranging from 3.3 ppmv to 4 ppmv, whereas an estimate based on an Eulerian mean calculation is about 6 ppmv. The amplitude of the annual cycle in water vapor mixing ratio at a potential temperature of 400 K in the tropics estimated from the Lagrangian calculation is compared with measurements of water vapor from the Halogen Occultation Experiment (HALOE). For the period 1992--2001, when HALOE measurements and ERA-40 data overlap, we calculate a peak-to-peak amplitude of ~1.7 ppmv, in good agreement with ~1.6 ppmv seen in HALOE data. On average, the Lagrangian calculations have a moist bias of ~0.2 ppmv, equivalent to a warm bias of the Lagrangian cold point of about 0.5 K. We conclude that the Lagrangian calculation based on synoptic-scale velocity and temperature fields yields estimates for stratospheric water vapor in good agreement with observations and that mesoscale and cloud microphysical processes need not be invoked, at first order, to explain annual mean and seasonal variation of water vapor mixing ratios in the tropical lower stratosphere.