State Department spokesman John Kirby says the Americans were among "several" people killed in the attack at the Jordan global Police Training Center near Amman.
Officials have released few details, but government spokesman Mohammed Momani said Tuesday that the attacker, a Jordanian police captain, opened fire in a dining hall.
It was not clear if there was a political motive for the shooting.
The company identified the South African killed in the shooting as Conrad Vaughn Whitehorn, 37, of Johannesburg, who previously had worked as a bodyguard and driver before joining DynCorp.
According to the January 2014 resume posted to his LinkedIn page, Fields served in the U.S. Army from 1988 to 1993.
Fields' wife, Tamara, could not be reached for comment on Tuesday.
Also killed was Lloyd "Carl" Fields, Jr., 46, of Cape Coral, who began working for DynCorp globally in 2006 as a police advisor in Iraq. The two wounded Americans are also civilians, the State Department said.
Jihadis called the attacker a martyr, according to the Middle East Media Research Institute.
Sajida al-Rishawi was arrested after the attacks and confessed that she was also wearing an explosives belt but had been unable to detonate it. She was tried and sentenced to death.
The American security company he worked for, DynCorp, said the 37-year-old was survived by his fiancée and his parents.
"The concerned authorities are in direct contact with their counterparts in the victims' countries, and we report progress in the investigations related to the incident to them", Government Spokesperson Mohammad Momani told The Jordan Times.
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Benito, in an email, said he "clearly remembered the after-season pool party and how proud his dad was his son and the championship we won".
"He was a great American who loved his family deeply".
Amman is a key ally of the United States, which announced in February its intention to increase overall USA assistance to Jordan from $660 million to $1 billion annually for the 2015-2017 period.
