An official source said on Sunday that the country's Council of Ministers made the historic decision.
Four men were also appointed to the 16-member body, six of whose members are named by decree.
The state news agency, Kuna, named the women as Shaikha Fatima al-Sabah of the ruling family, an architect who is an assistant undersecretary at the office of the country's ruler, and Fawziya al-Bahar, an engineer.
Women were excluded from local polls on Thursday to elect the remaining 10 members because a law passed in May allowing them to vote and run in elections came too late for this round.
But women will be able to vote in the 2007 parliament elections and 2009 local polls.
Last month's suffrage bill was seen as a breakthrough in Kuwait, a strategic US ally that has pledged to pursue democratic reform.
Although Kuwaiti women have reached high positions in the oil industry, the education system and the diplomatic corps, the country's 1962 election law limited political rights to men.
Previously, only men over 21 who were not members of the police or the military were allowed to vote. This meant that just more than 139,000 people were registered to cast ballots out of 960,000 Kuwaitis.
But with women over 21 able to vote now, as stipulated under the new law, the figure could reach 339,000.