A White House statement issued from President George W. Bush's ranch in Crawford, Texas, said his administration had suspended proceedings against the two Britons and that no proceedings would be started against any Australian nationals before consultations with Canberra.
An official spokesman of the British prime minister said Bush listened to the concerns of Tony Blair and he believed this was the best way forward.
The Britons were among a group of six detainees at the US naval base in Cuba’s Guantanamo Bay. Washington had announced it would try the six in military tribunals, away from public scrutiny.
This decision had provoked protests from human rights groups, their friends and lawyers of the two Britons, 23-year-old Feroz Abbasi and 35-year-old Moazzam Begg.
Blair was under pressure to persuade Bush to reverse his position and allow the two suspects to face trial in the United Kingdom.
The rights groups and the friends and families of the two Britons feared they would not get a fair hearing and could end up with death sentences.
The London-based rights group Amnesty International had expressed concern that the tribunals would impose the death penalty - "an inhumane punishment outlawed in the UK and opposed by human rights campaigners around the world."
"The proposed tribunals do not comply with international law. They are not independent since their members are appointed by the US Executive," Amnesty said.
The UK government too had expressed concern about the men's access to lawyers, the standards of evidence and their rights to appeal in the case of an adverse verdict.
The decision on the British detainees is expected to have implications for the other foreigners being held in Cuba.
'The proposed tribunals do not comply with international law.'
-- Amnesty International
There are seven other Britons in Guantanamo, but they were not in the group that was chosen to appear before a military tribunal.
The US set up the Guantanamo Bay detention centre in 2002 to hold suspected al-Qaeda members captured during the invasion of Afghanistan.
At least 680 men are being held there in clear breach of the Geneva Conventions.
The United States also said on Friday it had released 37 prisoners and they were being flown to Afghanistan.