The prime minister, who has admitted to following the Ashes series closely, said: "I've spoken to Andrew Strauss this morning and congratulated the team, coaches and everyone behind the side on this tremendous victory.
"Retaining the Ashes was a fantastic achievement, but winning the series really is the icing on the cake.
"We've seen some great sporting moments over the series and the team have provided us with some brilliant memories that I'm sure fans will talk about for years to come." Cameron said the whole country was "incredibly proud" of the team.
Meanwhile, Cameron White was named as skipper of Australia's team on Friday for next week's two Twenty20 internationals with England after the sudden retirement of Michael Clarke.
Clarke announced he was quitting international T20 cricket immediately after Australia's humiliating Ashes series loss to England on Friday, saying he wanted to improve his Test form.
Brad Haddin, Clarke's vice-captain in the Sydney Test, was left out of the T20 team for younger wicketkeeper rival Tim Paine, who will be the team deputy to White.
"Michael's decision is a personal one and done for the right reasons for him," chairman of selectors Andrew Hilditch said.
"The reality is he's a critical player for us moving forward, playing all three forms of the game.
"Michael hasn't had a break in a long time, so creating a window for him to get time off cricket is a good idea, but that was Michael's decision.
"If Michael thought he was ready he would play all three forms of the game." Hilditch said selectors were using the opportunity to play Paine and it was not a reflection on Haddin's form.
Shane Watson, Steven Smith and Mitchell Johnson are the only members of Australia's Test team selected for the T20 games in Adelaide on January 12 and Melbourne on January 14.
: Cameron White (capt), Tim Paine (vice-capt), Aaron Finch, David Hussey, Mitchell Johnson, Brett Lee, Stephen O'Keefe, James Pattinson, Steven Smith, Shaun Tait, David Warner, Shane Watson.
In Colombo, Sri Lanka left out World Cup winners Sanath Jayasuriya and Chaminda Vaas from their final 15-man squad for this year's tournament.
Both players were named in the provisional squad of 30 but failed to make Friday's cut, leaving Muttiah Muralitharan as the only remaining member of the triumphant Sri Lanka team from 1996.
Kumar Sangakkara will lead Sri Lanka in the tournament being hosted by India, Sri Lanka and Bangladesh and running from Feb. 19 to April 2.
Left-arm spinner Rangana Herath managed to beat off-spinner Suraj Randiv in one of the few surprises in the final 15.
Kumar Sangakkara (captain), Mahela Jayawardene (vice-captain), Tillakaratne Dilshan, Upul Tharanga, Thilan Samaraweera, Chamara Silva, Chamara Kapugedera, Angelo Mathews, Thisara Perera, Nuwan Kulasekara, Lasith Malinga, Dilhara Fernando, Muttiah Muralitharan, Ajantha Mendis, Rangana Herath.
