A new Solicitor-General has been appointed after a stoush with Attorney-General George Brandis drove the previous one to resign.

Senator Brandis has announced Dr Stephen Donaghue QC will start in his role as Australia's second law officer on January 16, for a period of five years.

It comes weeks after Justin Gleeson resigned following a dispute with the Attorney-General over whether he was consulted on a legal change he said undermined his independence.

Senator Brandis said Dr Donaghue was a distinguished constitutional lawyer who had frequently appeared as senior counsel before the High Court.