His predecessor, John Howard, set up the Nauru centre to process asylum-seekers away from mainland Australia, but it was strongly criticised by rights groups at home and abroad.
The new government has said however that it would retain a tough border policy through a purpose-built detention centre on the remote Australian territory of Christmas Island in the Indian Ocean.
Richard Towle, regional head of the United Nations High Commissioner for Refugees, said the closure of the Nauru centre marked "the end of a long and fairly painful chapter in Australian asylum policy and practice".
"We're delighted that Nauru finally will have no more refugees on it from now on," he told Australian radio.
|The Nauru centre has processed more than|
1,300 asylum seekers since 2001 [AP]
Howard introduced the "Pacific Solution" policy in late 2001 following a standoff involving 439 mostly-Afghan refugees who were blocked from landing in Australia by special forces soldiers.
A Norwegian freighter, the MV Tampa, had rescued the Afghans at sea after their fishing vessel sank in international waters en route to Australia.
More than 1,300 asylum seekers were processed on Nauru during its six years in operation, while others were sent to Manus Island in Papua New Guinea in return for millions of dollars in Australian aid.
The Labor government said the policy had wasted more than A$300m (US$268m) since its inception.
But in Nauru itself the shutdown has raised concerns about the island's economic future which the government has warned could be "at risk of collapsing again".
The entire economy recovered from the brink of ruin after signing the deal with Australia to open the centre in 2001, in addition to receiving A$15m in aid.
The island's cash-strapped government wants Australia to increase aid to compensate for potentially losing an estimated one-fifth of its GDP as a result of the shutdown.