The law will cut the number of constituencies from 25 to five as called for by opposition MPs who hope that this will reduce vote-buying under the old electoral boundaries.
A previous bill recommending the changes was rejected by the previous cabinet, triggering a row that led to the dissolution of parliament and last month's elections.
The cabinet sent the draft to the amir for approval before sending it to parliament for a vote.
The parliament, dominated by reformist MPs, convenes on Wednesday to elect a speaker.
The 16-member cabinet, which includes a woman minister and is dominated by members of Kuwait's ruling family, took the oath of office before the amir of Kuwait, Sheikh Sabah al-Ahmed al-Sabah.
Two former ministers who had faced opposition allegations of corruption and blocking reforms were dropped from the new cabinet.
Sheikh Ahmed Fahd al-Sabah, a nephew of the amir who held the key energy portfolio, and Mohammed Daifallah Sharar, who was state minister for cabinet, were transferred to new roles outside the cabinet.