At least two of the defendants were child offenders when they allegedly robbed jewelry stores at gunpoint in 2005, Human Rights Watch said.
The men, ages 20 to 24, "were severely beaten, denied food and water, deprived of sleep, forced to remain standing for 24 hours and then forced to sign 'confessions," Amnesty International said.
The men themselves said they were denied legal assistance and were not allowed to defend themselves during their trial, the Sabq Arabic news agency reported.
They have been under a death sentence since August 2009.
"We were in a period of adolescence and ignorance, and we all regret what we have done," defendant Yasser al-Otaibi told the news agency, explaining they have all since found God and now know the Koran completely.
"Please reverse the judgment for lack of lawyers to us during judgment," Otaibi said.
The Court of Cassation, a top appellate court, ruled the seven amounted to a gang. It affirmed a lower court's death sentence.
Saudi Arabia follows a strict version of Sharia, or Islamic law.
Abdullah, 89, Saturday authorized the death sentences to be carried out and sent the men to the southwestern Saudi city of Abha.
Abha is the capital of the rustic Asir province, where the men are from.
The alleged gang leader is to be crucified for three days, authorities said. The six others are to face firing squads.
Washington's Institute for Gulf Affairs rights-advocacy group told the U.N. High Commissioner for Human Rights in a statement, "Among the reasons for the execution is that [the men] hail from the south, a region that is heavily marginalized by the Saudi monarchy, which views them as lower-class citizens."