The low-lying coastal and island regions are vulnerable to sea level rise and extreme events. Compounded by marine heatwaves, sea level extremes have devastating impacts on coastal community and marine ecosystems. As long tide gauge records are sparse, sea level extremes around Indonesia are poorly understood, and the Compound Height-Heat EXtreme events remain unexplored. Here we combine in situ and satellite observations with model simulations, to investigate the long-lasting (>1 month) sea level extremes and C-HHEXs along Indonesian coasts of the Indian Ocean since the 1960s. We find that 90% (80%) of the extreme sea level events, with a maximum monthly sea level anomaly of 0.45m, are concentrated in an 8yr period of 2010-2017, due to anthropogenic global sea level rise and decadal enhancements by wind-driven ocean circulation. Remote and local surface wind anomalies associated with negative phases of the Indian Ocean Dipole (IOD) - enhanced by La Niña for some events – drive individual compound extreme events. By contrast, winds associated with monsoon intraseasonal oscillations force the sea level alone events. The shoaling thermocline in eastern equatorial Indian Ocean under anthropogenic warming favorably precondition the ocean for stronger and more frequent sea level extreme and heatwave compounds, increasing the environmental stress on Indonesia.