The subtropical highs are semi-permanent atmospheric features that strengthen during April-September and exert large influences on regional precipitation. Previous studies of their future changes mainly focused on their peak season (June-August). Here we find a robust seasonally-dependent response of the subtropical highs to warming in a suite of multi-model simulations. Both the North Pacific and North Atlantic subtropical highs strengthen more in April-June than July-September, with opposite changes in the Southern Hemispheric counterpart. These seasonally dependent responses of North Pacific and North Atlantic subtropical highs are mainly contributed by their zonal-mean component. Meanwhile, these responses are closely related to a southward shift of tropical precipitation in April-June relative to July-September, manifesting in a seasonal delay of tropical precipitation and monsoon rainfall onset in the Northern Hemisphere. From theory and analysis of atmospheric energetics, it is found that in a warmer world, the Northern Hemisphere needs more latent energy to warm up during April-June as constrained by the Clausius-Clapeyron relation, and the opposite occurs in the Southern Hemisphere. The interhemispheric energy contrast drives a southward shift of tropical precipitation that strengthens the Hadley cell and the subtropical highs in the Northern Hemisphere in April-June. These changes scale linearly with warming, so they have increasing implications for projecting regional climate changes in the tropics and subtropics as the warming continues.