The climate change attribution problem is addressed using empirical decomposition. Cycles in solar motion and activity of 60 and 20 years were used to develop an empirical model of Earth temperature variations. The model was fit to the Hadley global temperature data up to 1950 (time period before anthropogenic emissions became the dominant forcing mechanism), and then extrapolated from 1951 to 2010. The residuals showed an approximate linear upward trend of about 0.66°C/century from 1942 to 2010. Herein we assume that this residual upward warming has been mostly induced by anthropogenic emissions, urbanization and land use change. The warming observed before 1942 is relatively small and is assumed to have been mostly naturally induced. The resulting full natural plus anthropogenic model fits the entire 160 year record very well. Residual analysis does not provide any evidence for a substantial cooling effect due to sulfate aerosols from 1940 to 1970. The cooling observed during that period may be due to a natural 60-year cycle, which is visible in the global temperature since 1850 and has been observed also in numerous multisecular climatic records. New solar activity proxy models are developed that suggest a mechanism for both the 60-year climate cycle and a portion of the long-term warming trend. Our results suggest that because current models underestimate the strength of natural multidecadal cycles in the temperature records, the anthropogenic contribution to climate change since 1850 should be less than half of that previously claimed by the IPCC. About 60% of the warming observed from 1970 to 2000 was very likely caused by the above natural 60-year climatic cycle during its warming phase. A 21st Century forecast suggests that climate may remain approximately steady until 2030-2040, and may at most warm 0.5-1.0°C by 2100 at the estimated 0.66°C/century anthropogenic warming rate, which is about 3.5 times smaller than the average 2.3°C/century anthropogenic warming rate projected by the IPCC up to the first decades of the 21st century. However, additional multisecular natural cycles may cool the climate further.