The government says the bill, passed in the early morning hours, will merely enshrine into law Israel's existing character.
Prime Minister Benjamin Netanyahu called the legislation's passage a "historic moment in the history of Zionism and the history of the state of Israel."
"Israel is the nation state of the Jewish people, which honors the individual rights of all its citizens," the prime minister said. "I repeat this is our state. The Jewish state."
"Lately, there are people who are trying to destabilize this and therefore destabilize the foundations of our existence and our rights," he added. "So today we have made a law in stone. This is our country. This is our language. This is our anthem and this is our flag. Long live the state of Israel."
But opponents to the law say it marginalizes the country's Arab minority. One clause downgrades the Arabic language from official to "special" standing. Around 20 percent of Israel's population is Arab.
The law passed with a 62-55 backing, with two members of the Knesset, Israel's parliament, abstaining. The legislation is defined as a "basic law," granting it quasi-constitutional status.
However, it will likely face a challenge at the Supreme Court.
Politicians took turns to passionately express their views for and against the bill in a rowdy, hours-long debate in parliament overnight.
Ayman Odeh, the head of the Arab Joint List, pulled out a black flag and waved it during his speech in parliament, warning of the implications of the law.
"This is an evil law," he said and added that "a black flag hovers over it."
"Today, I will have to tell my children, along with all the children of Palestinian Arab towns in the country, that the state has declared that it does not want us here," Odeh said in a statement following the law's passage.
"It has passed a law of Jewish supremacy and told us that we will always be second-class citizens," the statement said.
Benny Begin, son of former Israeli prime minister Menachem Begin, the founder of Netanyahu's ruling Likud party, abstained from voting, warning of the party's growing disconnect from human rights.
"This is not a decision I expected from the Likud leadership," he said.
American Jewish organizations also expressed disapproval of the law.
The American Jewish Committee, a group representing the Jewish Diaspora, said it was "deeply disappointed," saying the law "put at risk the commitment of Israel's founders to build a country that is both Jewish and democratic."
Lawmakers had removed the most contentious clause of the bill on Sunday, which would have allowed the establishment of "separate communities," and whose inclusion critics had called racist.
Israelis, including President Reuven Rivlin and attorney general, voiced opposition to the earlier draft of the bill.
