Prime Minister Lee Hsien Loong was given a ceremonial welcome to Canberra.
The first Singaporean leader to address the national parliament reflected on more than 50 years of diplomatic ties with Australia.
"We are good friends because, fundamentally, we have similar strategic interests and perspectives. First, we are both open economies that rely heavily on international trade, on global markets. We both need a stable and orderly world in which countries big and small can prosper in peace."
Singapore is Australia's largest trading partner in south-east Asia.
A city-state smaller than Canberra, it already rotates 6,000 of its troops through Australia.
Under a new deal, the number will increase to 14,000 annually.
Prime Minister Malcolm Turnbull told his Singaporean counterpart they share common ambitions.
"To ensure our countries are more innovative, more productive, more competitive. I valued enormously his counsel on regional affairs to which he brings the wisdom of many years in government."
Defence Industry Minister Christopher Pyne says Singapore will fully fund the redevelopment of army Barracks in North Queensland to accommodate the extra troops.
"Spending $2.25 billion in north Queensland to develop those training facilities. Around one billion dollars at Shoalwater Bay training area and about a billion dollars at Townsville field training area and its environments. Australia will also grant Singapore enhanced access for unilateral land training."
Prime Minister Loong also used the occasion to address regional engagement with China - a major trading partner for Singapore and Australia's largest overall.
"We wish to strengthen our cooperation with China and welcome China in engaging constructively with the region."
Chinese tabloids and state media have recently criticised the Singaporean government over its views on territorial disputes in the South China Sea.
John Blaxland is from the Defence Studies Centre at the Australian National University in Canberra.
He says Singapore's leadership is not afraid of addressing delicate and sometimes uncomfortable strategic issues.
"Singapore calls the shots, it calls a spade a spade, it's not afraid to call it the way it sees it. It does that because it's confident in its place in the world and its relationship with great powers and China seems to be unhappy about that."
The two leaders will sign a deal to update the 2003 free trade agreement - which helped make Singapore Australia's fifth largest trading partner - and improve exchanges in the areas of innovation, science, education and the arts.
