Al Jazeera's Rob Reynolds says the issue of harsh treastment of detainees will no doubt be brought up as Ghailani was held for a period of time in some of the CIA's so-called "black site" prisons before being transferred to Guantanamo.
The question raised by his trial is whether the US court system can try someone held under such circumstances who may have been subjected to harsh interrogation techniques many describe as torture, he says.
A total of 213 people were killed in Nairobi, Kenya, and 11 people died and at least 85 were wounded in the Tanzania bombing in the city of Dar-es-Salaam in attacks widely blamed on Osama bin Laden's al-Qaeda network.
"This should be a model for other cases as well - suspects should be brought to civilian courts, which are tried and tested and which get the job done"
Zachary Katznelson, legal director of Reprieve
Ghailani is accused of helping to buy a lorry and oxygen and acetylene tanks that were used in the Tanzania bombing, and of allegedly loading boxes of TNT, detonators and other equipment into the vehicle in the weeks running up to the bombing.
Ghailani reportedly confessed at a 2007 hearing at Guantanamo Bay and apologised for supplying equipment used in the bombing, but said he did not know the supplies would be used to attack the embassy, according to military transcripts.
Zachary Katznelson, the legal director of Reprieve, a London-based group of human rights lawyers who work on Guantanamo cases, welcomed the move to try Ghailani in a US court.
He told the Reuters news agency: "This should be a model for other cases as well.
"Suspects should be brought to civilian courts, which are tried and tested and which get the job done, rather to military courts where they are essentially making it up as they go along."
The decision to bring Ghailani to trial in New York follows a review by the Guantanamo Review Task Force of 240 foreign "terror" suspects still held at Guantanamo, ordered by Barack Obama, the US president.
Obama has also ordered the Guantanamo Bay prison, set up by the administration of his predecessor George Bush following the September 11 attacks in New York in 2001, to be closed by the end of January next year.
The US president hopes other countries will take in some of the 50 detainees so far cleared for release. However, many have refused.
Members of the US Congress also objected to the inmates being transferred to US prisons, saying they were potential "security risks".