Australia, in turn, may resettle an unspecified number of Cuban and Haitian asylum seekers also intercepted at sea and sent to US detention facilities at Guantanamo Bay, Cuba.
Howard said the refugee swap would deter potential illegal migrants to Australia or the US, by denying them their intended destination country.
But critics have said the plan could actually encourage asylum seekers.
Speaking to Australia's ABC radio, Howard said the move was "part of our policy to reinforce the message to those who would engage in people smuggling that this country has a tough border protection policy".
Illegal immigration has been a focus of intense political debate in Australia since the 1990s, when a wave of asylum seekers reached Australia's northern shores in rickety boats launched from nearby Indonesia.
In response, Canberra toughened its immigration laws in 2001, setting up a network of prison-like immigration detention camps across the country.
Last year, Howard tightened the government's stance further, announcing that any asylum seekers who reach Australia by boat would be sent to detention centres in Nauru and neighbouring Papua New Guinea while their refugee claims are processed.
Asked how the proposed swap would deter future asylum seekers, Howard responded: "The thing that discourages people from people smuggling is the fact that we make it very plain that people will not be allowed to reach the Australian mainland."
Asylum seekers held in Australian detention camps can be held for months, sometimes years, before their claims are processed.
Australia has come under fierce criticism from human rights groups for its strict immigration policies.
Critics say the offshore centres keep refugees out of sight and out of mind, and that by sending Australia's asylum seekers to the United States, Howard will not have to address the politically sensitive issue of keeping legitimate refugees in detention centres for lengthy periods.
According to Wednesday's edition of The Australian newspaper, 83 Sri Lankans and eight people from Myanmar would be the first refugees to be sent to the United States.
About 200 refugees will be processed in each country every year, it said.