If approved, Hicks' legal team will argue that he should be released from US detention under an agreement between the US and UK that no British citizen face the US military commission process.
"We are quietly confident that we will get a favourable decision," when the High Court hands down its decision at 10am GMT (9pm AEDT) on Tuesday, lawyer David McLeod told AFP.
David Hicks, 30, was arrested four years ago in Afghanistan in the wake of the US-led invasion prompted by the September 11, 2001 attacks in the United States.
He has pleaded not guilty to charges of conspiracy, attempted murder and aiding the enemy, and is due to face a military commission hearing at an unspecified date.
He applied for British citizenship earlier this year after an off-hand revelation to one of his US lawyers that his mother had been born in England and had lived there as a child.
Hicks' first application was refused by British Home Secretary Charles Clarke but Mr McLeod said he is hopeful that will be reversed on appeal.
The refusal was on the basis that Hicks had allegedly performed "an act prejudicial to the interests of the United Kingdom" by attending terrorist training camps in Afghanistan and Pakistan, but his lawyer said citizenship is a matter of right, not discretion.
"Conduct does not come into it," he said.
"We would simply inform the US government that there is another UK citizen in their gulag in Guantanamo and we would rather they hand him over shortly," said Mr McLeod.
The Law Council of Australia said it is a travesty that Hicks has been forced to seek British citizenship because the Australian government has turned its back on him.
"It is clear that... our government has well and truly washed its hands of one of its own citizens," council president John North said.
"An Australian who has spent so long in legal limbo should not have to plead to another nation's government for help."
Meanwhile, American Catholic peace activists have arrived at the perimeter fence of Guantanamo Bay's US naval base to begin a three-day fast and vigil protesting against conditions for terrorism suspects held there.
The protest coincides with growing international demands from politicians, human rights organisations, the Red Cross and others to see Guantanamo detainees.
The demand comes because of accusations they are being cruelly treated.