Vegetation productivity in India varies at intraseasonal to interannual time scales, influenced by meteorological factors sensitive to large-scale climate teleconnections. While the impact of global climate variability on Indian monsoon and its extremes is well known, their effects on Indian vegetation productivity are relatively less understood. This study addresses this gap by decomposing dominant modes of spatio-temporal variability of gross primary productivity (GPP) over India and examining their dependence on climate teleconnections. We found that El-Niño Southern Oscillation (ENSO) and Pacific Meridional Mode (PMM) significantly impact GPP, especially in western and southern peninsular India during the monsoon and post-monsoon seasons. However, there is an east-west asymmetry in the PMM-GPP correlation. The western region and southern peninsula are negatively correlated, while northeast India positively correlates with PMM. Using wavelet decomposition, we show that more than half of temporal variability in the GPP comprises low-frequency components. These low-frequency signals primarily drive the relationship between GPP and climate teleconnections. Next, we identify the dominant spatial modes of low-frequency signals of GPP. We tested the predictability of the principal components of GPP using teleconnections and hydrometeorological variables. While most of the predictive skill of GPP comes from its past (memory up to 5 months, R2 score of up to 0.5), adding teleconnection indices as predictors improves the prediction skill at lead times (with an increase of 0.1-0.2 in R2 values). Our results underscore the utility of using hydrometeorological and distant climate teleconnection in GPP prediction for longer lead times.