Sabah al-Ahmad, the half-brother of the late Emir Sheikh Jaber al-Ahmad, is the first person to become ruler of a Gulf State through constitutional means, the BBC said. He has been effectively running the country for several years during his brother's illness.
Sheikh Saad al-Abdullah became emir nine days ago when Jaber al-Ahmad died. But he is also in ill health.
The succession threatened to create a nasty feud between the two branches of the ruling family, which alternate as emir under an agreement cobbled out a century ago. Members of parliament were also reluctant to oust Saad al-Abdullah, who remains popular because of his actions after the Iraqi invasion.
Saad al-Abdullah resolved the crisis by sending the Cabinet a letter announcing his abdication.
Kuwait has 10 percent of the world's proven oil reserves, giving the emirate an importance out of proportion to its size.