Until now the selection panels for these Crown posts have comprised the Lieutenant Governor, a Deemster and the Chief Minister.
In future the panels will consist of the First Deemster (or First Deemster Designate or Judge of Appeal), the Chief Minister and the President of Tynwald.
The panels will make recommendations to the UK Secretary of State for Justice for appointment by Her Majesty.
The move follows the announcement in July this year that the next Lieutenant Governor would be selected by an entirely local interview panel – comprising the Chief Minister, President of Tynwald and the First Deemster – instead of a panel dominated by UK representatives.
The Chief Minister said: 'Increasing the involvement of Island representatives in the recruitment process for these important Crown appointments is another small but quite significant step forward in the continuing constitutional advancement of the Isle of Man.'
The new process will be used for the first time in the recruitment of the next First Deemster, following the death of His Honour Michael Kerruish QC, and of the next Attorney General – the current post holder John Corlett QC is due to retire in April next year.
Both positions will be advertised shortly. Rates of pay will be the same as they are at present.
Mr Brown said the moves towards the Island having greater responsibility for its own affairs was driven by the Island but the UK had been very amenable and positive about making the changes.
Asked whether with the further diminution of the role of the Lieutenant Governor meant that there was any real need for this post in the future, he replied: 'We are not going down the road of a republic unless one day we become independent.
'The Lieutenant Governor represents the Queen as head of State. It doesn't mean that the Isle of Man can't have greater control and influence on its own affairs.'