The United States and the United Nations have both welcomed Kuwait's decision to give full political rights to women as an important advance.
Government eroded opposition with a number of measures
The US state department said the change to election law would help not only women but the whole of Kuwaiti society.
A UN statement said: "The Secretary General congratulates the people of Kuwait on this historic step."
There were celebrations around the Gulf state on Monday after parliament agreed to let women vote and stand for office.
The result, announced by the speaker of parliament, was greeted with thunderous applause from the public gallery where backers of the amendment were gathered.
Outside, drivers hooted their horns, people danced and cheered and lit fireworks.
"We made it. This is history," said suffrage activist Roula Dashti.
"Our target is the parliamentary polls in 2007. I'm starting my campaign from today."
Previous delays in holding the vote mean that women will be unable to participate in local elections set for 2 June.
Islamist MPs, who foiled past suffrage moves, added a clause on Monday saying women must abide by Islamic law when voting and campaigning.
"I hope they are talking about separate ballot boxes and not the imposition of Islamic dress... which infringes on personal freedoms," Kuwait University academic Nada al-Muttawa said.
Some Islamists accused the government of pressurising MPs to pass the amendment to the electoral law, saying the change goes against religious teaching and serves US interests.
Kuwait becomes the fourth Gulf country where women as well as men can vote in elections after Bahrain, Oman and Qatar. Saudi Arabia holds strictly limited, male-only elections.
"Thank God we finished with this issue," Prime Minister Sheikh Sabah al-Ahmad al-Sabah said.
"I want our womenfolk to help us build our beloved country and our future."
Also on Monday, the cabinet approved a $445m (£242m) bill to raise salaries for public and private employees in a move analysts say was designed to soften the blow for conservatives.
The victory came as a surprise to many activists in the gallery
The cabinet's insistence on voting on the women's suffrage amendment took some lawmakers by surprise as they were expecting only to discuss moves to allow women limited participation in municipal elections due in 2009.
The Bush administration has been pressing its oil-rich and strategic Middle East allies to bring in reforms since the 11 September 2001 attacks on the US - arguing that political stagnation fuels terrorism.
"We think this is an important step forward for Kuwait, for the women of Kuwait and for the nation as a whole," said US state department spokesman Richard Boucher after Monday's vote.
Kuwait's ruler Sheikh Jabir al-Ahmad al-Sabah issued a decree giving women full political rights in 1999, but until now it has been successfully fended off by the tribal/Islamist alliance that dominates parliament.