Greenland ice sheet experienced an intensive melting in the last century, especially in the 1920s and over the last decades. The supplementary input into the ocean could disrupt the freshwater budget of the North Atlantic. Simultaneously, some signs of a recent weakening of the Atlantic Meridional Overturning Circulation (AMOC) have been reported. In order to better understand the possible impact of the increasing melting on the North Atlantic circulation, salinity and temperature trends, we construct an observation-based estimate of the freshwater fluxes spanning from 1840 to 2014. The estimate is based on runoff fluxes coming from Greenland ice sheet and surrounding glaciers and ice caps. Input from iceberg melting is also included and spatially distributed over the North Atlantic following an observed climatology. We force a set of historical simulations of the IPSL-CM6A-LR coupled climate model with this reconstruction from 1920 to 2014. The ten-member ensemble mean displays freshened and cooled waters around Greenland, which spread in the subpolar gyre, and then towards the subtropical gyre and the Nordic Seas. Over the whole period, the convection is reduced in the Labrador and Nordic Seas, while it is slightly enhanced in the Irminger Sea, and the AMOC is weakened by 0.32±0.35 Sv at 26°N. The multi-decadal trend of the North Atlantic surface temperature obtained with the additional freshwater forcing is slightly closer to observations than in standard historical simulations, although the two trends are only different at the 90% confidence level. Slight improvement of the Root Mean Square Error with respect to observations in the subpolar gyre region suggests that part of the surface temperature variability over the recent decades may have been forced by the release of freshwater from Greenland and surrounding regions since the 1920s. Finally, we highlight that the AMOC decrease due to Greenland melting remains modest in these simulations and can only explain a very small amount of the 3±1 Sv weakening suggested in a recent study.