Justice Stephen Gageler to become next High Court chief

"He is highly respected for his leadership abilities and deep knowledge and understanding of constitutional law," they said in a statement on Tuesday.

The judge is the most senior puisne of the court, having served since 2012. 

Justice Gageler is a former commonwealth solicitor-general, having been admitted as a barrister of the NSW Supreme Court in 1989 and senior counsel in 2000.

NSW Supreme Court judge Robert Beech-Jones will fill the seat left by Justice Gageler, also starting on November 6.

Mr Albanese 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. 

Shadow attorney-general Michaelia Cash welcomed the appointments.

"The coalition congratulates Justice Stephen Gageler on his appointment as Chief Justice of the High Court of Australia and recognises his extensive experience both as a High Court justice and previously as Australia's solicitor-general," she said.

"The coalition congratulates Justice Robert Beech-Jones on his appointment to the High Court and acknowledges his long service as a justice of the Supreme Court of NSW and as chief justice of common law."

NSW chief justice Andrew Bell also had praise for the appointments.

"Both judges are universally admired and respected for their outstanding legal ability, the quality of their judgments, their integrity and humility, and strong sense of public service," he said.

"Of Chief Justice-elect Gageler it may fairly be said that there is no practising lawyer in this country with a deeper knowledge of the Australian constitution."