The change in the leadership of the ruling Labor Party comes just months ahead of a general election.
Ms Gillard's swearing in as prime minister will be a formality.
"I feel very honoured, I will be making a full statement very shortly," she told reporters after emerging from a party meeting at Parliament House in Canberra.
A party spokesman said Ms Gillard had stood unopposed at a vote of the Labor Party's 112 members of parliament at a meeting on Thursday morning.
