Proxy climate data from the Greenland icecap and marine deposits in the Pacific indicate that warm conditions in the North Atlantic are linked to cool conditions in the Eastern Equatorial Pacific, and vice versa. Our ocean models show that the surface branch of the overturning circulation connecting the North Atlantic to the Equatorial Pacific adjusts by exchanging thermocline water between ocean basins in response to changes in deep water formation in the northern North Atlantic. Planetary ocean waves give rise to a global oceanic seiche, such that the volume of thermocline water decreases in the Pacific-Indian Ocean while increasing in the Atlantic Ocean. We conjecture that the remotely forced changes in the thermocline of the Eastern Equatorial Pacific may trigger El Niño events. These global seiches have been previously overlooked due to the difficulty of integrating high-resolution climate models for very long time-scales.