Senator Amanda Vanstone was stripped of indigenous affairs in Prime Minister John Howard's cabinet reshuffle.
The role was handed to Mr Brough, who takes on the redesigned portfolio of families, community services and indigenous affairs.
Mr Brough, the former assistant treasurer, said he was committed to achieving real outcomes for indigenous Australians.
"I've always been outcome-focussed in any of the portfolios that I've held and what I would view as success here is improved health outcomes, improved educational outcomes, improved self-esteem and improved opportunities," he told ABC radio.
"What I can assure everybody - the Australian public and the indigenous community in particular - is they've got a minister here, like those that have gone before, who will give 110 per cent to their needs.
"By doing so, they can be assured that they'll be listened to and that actions will be taken."
But Mr Brough backed away from suggestions he was seeking to assimilate Aboriginal people into wider Australian society.
"I'm not about to make any of those sort of statements," he said.
Australian Democrats' indigenous affairs spokesman Andrew Bartlett said because indigenous affairs was such an important issue in Australia, it should have been given a separate portfolio.
"It's clear for everybody that wants to look that indigenous affairs is probably the area of biggest policy failure of all political parties across the spectrum for decades now," Senator Bartlett told ABC Radio.
"You cannot have one group of people in the community who live 20 years less than the rest of us on average, that should be a national scandal and it should be given total priority."