Global climate change is a pressing problem caused by the accumulation of anthropogenic greenhouse gas emissions in the atmosphere. Carbon dioxide (CO2) capture and storage is a promising component of a portfolio of options to stabilize atmospheric CO2 concentrations. Meaningful capture and storage requires the permanent isolation of enormous amounts of CO2 away from the atmosphere. We investigate the effectiveness of heterogeneity-induced trapping mechanism, in potential synergy with a self-sealing gravitational trapping mechanism, for secure CO2 storage in marine sediments. We conduct the first comprehensive study on heterogeneous marine sediments with various thicknesses at various ocean depths. Prior studies of gravitational trapping have assumed homogeneous (deep-sea) sediments, but numerous studies suggest reservoir heterogeneity may enhance CO2 trapping. Heterogeneity can deter the upward migration of CO2 and prevent leakage through the seafloor into the seawater. Using geostatistically-based Monte Carlo simulations of CO2 transport in heterogeneous sediment, we show that strong spatial variability in permeability is a dominant physical mechanism for secure CO2 storage in marine sediments below 1.2 km water depth (less than half of the depth needed for the gravitational trapping). We identify thresholds for sediment thickness, mean permeability and porosity, and their relationships to meaningful injection rates. Our results for the U.S. Gulf of Mexico suggest that heterogeneity-assisted trapping has a greater areal extent with more than three times the CO2 storage capacity for secure offshore CO2 storage than with gravitational trapping. These characteristics offer CO2 storage opportunities that are closer to coasts, more accessible, and likely to be less costly.