Developing forest carbon sinks (FCS) is significant for China to achieve carbon neutrality. The Yellow River Basin is a principal area for China’s energy consumption, and the forest resource distribution of this vast basin is spatially dependent, determining that the development of FCS cannot be separated geographically. Based on the spatial panel data of 69 prefecture-level cities in the Yellow River basin from 1988 to 2018, we used ESDA to reveal the spatial–temporal characteristics of FCS, and we established a spatial econometric model to investigate the transregional spillover effects of FCS. The results showed that: ① the overall FCS showed a gradually increasing trend, with a general distribution characteristic of “upstream > midstream > downstream” from 1988 to 2018. ②FCS presented an agglomeration distribution pattern with significant spatial spillover effects, and the degree of uneven spatial agglomeration varied across the years. ③Urbanization rate, forestry fixed assets investment, labor input, and afforestation management level directly promote FCS growth, whereas forest harvesting, precipitation, and temperature decrease FCS. ④Urbanization rate, forest harvesting, forestry fixed assets investment, labor input, and afforestation management level have positive spillover effects on FCS, while precipitation and temperature have adverse spillover effects on FCS. Hence, pertinent policy suggestions are put out to serve as a guide for increasing FCS.