According to the Central Tibetan Administration, Dr Sangay also thanked the people and government of the two countries for their long-standing support for the Tibetan people.
"On behalf of the Tibetan people, I would like to congratulate you on your landslide victory in the election 2013 federal election and wish you all the success as the prime minister of Australia," Sikyong Dr. Lobsang Sangay wrote in his congratulatory letter to Prime Minister-elect Tony Abbott.
"The Central Tibetan Administration expresses its sincere for your support and meeting with His Holiness the Dalai Lama in December 2009.
"We welcome your Party's call for peaceful dialogue between China and Tibetan representatives to ensure Chinese respect for human rights and wish to reiterate our firm commitment to resolving the Tibet issue peacefully through dialogue.
"I thank the people and government of Australia for their long-standing support for democracy and non-violent struggle of the Tibetan people, and for granting asylums for Tibetans. I look forward to your continued support, under your leadership, for the issue of Tibet," Sikyong said.
The Tibetan political leader also congratulated Norway's Prime Minister-elect, Ms Erna Solberg, on her election win and wished her success in her future endeavours.
"I thank the people and government for their long-standing support for democracy and non-violent struggle of the Tibetan people. I look forward to your continued support, under your leadership, for the issue of Tibet," Sikyong said in his congratulatory message.