In a statement released on Tuesday, Prime Minister Anthony Albanese and Attorney-General Mark Dreyfus announced the appointment of the 14th High Court chief justice.
Justice Gageler is described as having an "outstanding reputation as a jurist".
"He is highly respected for his leadership abilities and deep knowledge and understanding of constitutional law," the statement reads.
The judge is the most senior puisne of the court, having served on it since 2012.
Previously, Justice Gageler was the commonwealth solicitor-general.
He was admitted as a barrister of the Supreme Court of New South Wales in 1989, and was appointed senior counsel in 2000.
Justice Robert Beech-Jones will be appointed to the High Court to fill the seat left by Justice Gageler, and will also start on November 6.
The prime minister and Mr Dreyfus thanked the nation's first female chief justice for her "exceptional service".
"On behalf of the government and the Australian people, we congratulate Justice Gageler and Justice Beech-Jones on their appointments, and wish Chief Justice Kiefel all the very best for the future," they said.
The government said Justice Gageler and Justice Beech-Jones were strongly supported during a consultation process for the appointments.
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