Prime Minister Benjamin Netanyahu's Cabinet voted to expand his coalition and appoint Lieberman, before the 120-seat Knesset approved him by a vote of 55-43.
Netanyahu, who has been accused of forming the most rightwing government in Israeli history, was forced to resolve a last-minute dispute with another party in his coalition to see the move through.
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Lieberman, a former foreign minister known for his provocative comments, has pledged harsh measures against Palestinian "terrorists" but has also promised to act in a "responsible" manner while in office.
He recently said he would give Ismail Haniya, the Hamas leader in Gaza, 48 hours to hand over two detained Israeli civilians and the bodies of soldiers killed in the 2014 war "or you're dead".
On Tuedsay Netanyahu said, "we will continue with a responsible and assertive security policy... And at the same time, will look for paths to peace, especially through regional developments, which we not only recognise but are also involved in."
Netanyahu's moves have drawn concern both inside Israel and abroad.
The United States has said the new coalition raises "legitimate questions" about the commitment of Netanyahu's government to a two-state solution with the Palestinians.
In the wake of the agreement, Environment Minister Avi Gabbay of the centre-right Kulanu party announced his resignation, saying: "I do not think it is right... To form an extremist government."
Before that, Lieberman's predecessor Moshe Yaalon, from Netanyahu's Likud, warned of a rising tide of extremism in the party and Israel as a whole when he resigned as defence minister on May 20.
However, Netanyahu's troubles also went beyond such criticism, with the vote to expand his coalition opening up previous fissures in his government.
The religious nationalist party Jewish Home had planned to vote against Lieberman's Yisrael Beitenu party in parliament, possibly sparking fresh elections, unless demands for procedural reform were met.
Jewish Home holds eight parliamentary seats, enough to block Netanyahu's new line-up.
Netanyahu and Jewish Home party leader Naftali Bennett reached a compromise on Sunday night.
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