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More than 90% of the Earth's energy imbalance is stored by the ocean. While previous studies have shown that changes in the ocean warming are detectable and distinct from internal variability of the climate system, an estimate of separate contributions by natural and individual anthropogenic forcings (such as greenhouse gases and aerosols) remains outstanding. Here we investigate anthropogenic and greenhouse-gas contributions to past ocean warming, and estimate their contributions to future sea level rise by the year 2100. By applying detection and attribution framework (regularized optimal fingerprinting), we show that ocean warming in the historical period is detectable and attributable to contributions from the aggregate anthropogenic forcing as well as greenhouse gas forcing alone. We also discuss the role of natural forcing on the ocean volume-averaged temperature and examine the impact of volcanic activity from the three main volcanoes occurring in the historical period 1955-2012. Our results suggest that estimated anthropogenic and greenhouse-gas contributions to ocean warming are consistent with observations, and observationally-constrained future thermosteric sea level rise projections support the central and lower part of the multi-model mean projection range distribution.