Ms Gillard was delivered power after weeks of negotiations when independent MPs Tony Windsor and Rob Oakeshott announced they would support a Labor minority government.
"I believe Julia Gillard is the right person to manage this new style of government," Mr Brumby said.
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"As I have always said, Julia Gillard will be a good prime minister for Victoria and for the nation."
Ms Gillard served as Mr Brumby's chief of staff in the 1990s.
"On a personal note, I am happy for Julia as a good friend," the premier said.
"She is a proud Victorian, a hard worker and a person of great principle."
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