The decision, based on a proposal by Jewish Agency chairman Natan Sharansky, was welcomed by liberal Jewish movements but condemned by ultra-Orthodox leaders, whose cabinet representatives voted against it.
The new prayer section would enable men and women to pray together in a space comprising hundreds of square metres (square yards) around the archaeological site known as Robinson's Arch, which has over the years hosted egalitarian ceremonies.
It is separated by the traditional women's and men's adjacent prayer sections by the ramp leading up to the Mughrabi Gate, the only entrance for non-Muslims to the flashpoint Al-Aqsa mosque compound, known to Jews as the Temple Mount.
Before the vote Prime Minister Benjamin Netanyahu called the arrangement "a compromise" and "a fair and creative solution".
The decision preempted a court discussion on a petition filed by Women of the Wall, activists who had insisted on their right to pray in the traditional women's section, despite the objections of the ultra-Orthodox rabbi who controls the holy site.
In accepting the compromise, Women of the Wall ceded their original demand, while forcing the state to acknowledge the right of non-Orthodox groups to worship at the site, the holiest place where Jews are legally allowed to pray.
"In approving this plan, the state acknowledges women's full equality and autonomy at the Kotel (Western Wall) and the imperative of freedom of choice in Judaism in Israel," Women of the Wall wrote on their Facebook page.
Signup to our newsletter and follow us on Facebook and Twitter!
The debate, which Women of the Wall say has lasted for 27 years, had raised tensions between the government and United States Jewry, where the Reform and Conservative movements have significant clout.
"We applaud Israel's historic decision," a joint statement from the Conservative, Reform movements and Jewish Federations in the United States read.
"The decision sends a powerful message to Israelis and Jews across the Diaspora about the permanent value of Jewish pluralism and about what we can do when we work together."
The move was slammed by the ultra-Orthodox parties Shas and United Torah Judaism, who opposed it in the vote, as well as by Agriculture Minister Uri Ariel of the far-right Jewish Home, who called it "an affront to our tradition".
Western Wall Rabbi Shmuel Rabinovitz said he received the decision "with a heavy heart" since he disapproved of egalitarian prayer, but also "a sigh of relief" as the Women of the Wall would no longer be praying in the traditional women's section.
The new prayer section is estimated to cost 35 million shekels ($8.8 million, 8.1 million euros) funded by the government and Jewish Agency. The cabinet decision does not say how long implementing it will take.
The Western Wall is venerated by Jews as a remnant of a wall supporting the Second Temple complex, which was destroyed by the Romans in 70 AD.
On its other side is the compound housing the Dome of the Rock and Al-Aqsa mosque, Islam's third holiest site.
The compound is a deeply sensitive location where clashes frequently erupt between Palestinian worshippers and Israeli forces. Rumours of Israel's intention to change the status quo there fuelled the latest four-month wave of Palestinian violence.
Israeli authorities do not allow Jews to pray on the compound.