Sketch of Kelvin wave dynamics. Regions of low sea level are regions of low pressure. Currents follow isobars (shown in black).
On the western side of the ocean currents flow away from the equator, taking water away from the equatorward side of the low pressure regions. As a result the area on the equatorward side of the low sea level region is depleted of water; this brings the sea level down and moves the region of low sea level toward the equator.
On the eastern side of the ocean currents flow towards the equator, filling the low pressure regions on the equatorward side and deepening them on the poleward side. As a result the regions of low sea level move toward the poles.
At the equator the current moves westward in both hemispheres, filling the low pressure region in the west and deepening the sea level in the east. This produces eastward propagation of the low pressure region.
In all cases the direction of propagation of low pressure regions is the same as the direction of propagation of high pressure regions. (Compare this diagram with the behaviour of high pressure regions.)