Quantification of CO2 fluxes at the Earth's surface is required to evaluate the causes and drivers of observed increases in atmospheric CO2 concentrations. Atmospheric inversion models disaggregate observed variations in atmospheric CO2 concentration to variability in CO2 emissions and sinks. They require prior constraints fossil CO2 emissions. Here we describe GCP-GridFED (version 2019.1), a gridded fossil emissions dataset that is consistent with the national CO2 emissions reported by the Global Carbon Project (GCP). GCP-GridFEDv2019.1 provides monthly fossil CO2 emissions estimates for the period 1959-2018 at a spatial resolution of 0.1°. Estimates are provided separately for oil, coal and natural gas, for mixed international bunker fuels, and for the calcination of limestone during cement production. GCP-GridFED also includes gridded estimates of O2 uptake based on oxidative ratios for oil, coal and natural gas. It will be updated annually and made available for atmospheric inversions contributing to GCP global carbon budget assessments, thus aligning the prior constraints on top-down fossil CO2 emissions with the bottom-up estimates compiled by the GCP.