Maj. Gen. Michael Jeffery now holds the position.
The governor general - a fixture of Australia's federal government since it began in 1901 - fulfills a mainly ceremonial role, with ruling power held by Parliament. The role carries formal titles, however, including commander in chief of the military.
The British monarch appoints the governor general, though by convention the prime minister picks the sole candidate.
When Bryce takes up the role, it will be the first time the monarch - for the past 56 years Queen Elizabeth II - has been represented in Australia by a woman.
"It's taken us 107 years. It's been a while," Rudd told reporters in the capital, Canberra. "It's good that it's happened."
Australia is a constitutional monarchy and, like many former British colonies, retains close ties to the English royals. It is not the first Commonwealth country to appoint a woman as governor general, with New Zealand and Canada among nations that have done so before.
Rudd said Bryce had "an outstanding record of service to the entire Australian community. She ... has enjoyed a rich and dynamic career as a lawyer, academic and senior public office holder."
Bryce, 65, is from Rudd's home state of Queensland, where in 1965 she became one of the first women admitted to the legal bar in that state. She went on to become a law lecturer and later a senior bureaucrat in state and federal women's rights, childcare and anti-discrimination offices.
Bryce said it was a great honor to be the first woman appointed to the job.
"What this day says to Australian women and to Australian girls is that you can do anything, you can be anything, and it makes my heart sing to see women in so many diverse roles across our country," she said.
Rights groups welcomed the decision.
"It's wonderful we have at last got a government who's making conscious decisions to include women in leadership roles," said Jenni Colwill, a vice president the lobbying group National Foundation for Australian Women.
Bryce has been appointed to a five-year term.
Rudd, who met Queen Elizabeth this month in London, is a supporter of a movement to make Australia a republic and to cut its last ties to the British monarchy. He would not comment Sunday, however, on whether Australia's first woman governor general could be its last.
"The move to a republic is not a top-order question for the government," Rudd said. "There are many other priorities around."
Although largely a ceremonial role, the governor general does have power. In 1975, then-Governor General Sir John Kerr used constitutional powers to sensationally dismiss Prime Minister Gough Whitlam's government over budget problems.