Citing US officials familiar with the matter, the report said the strike was the third Iranian missile attack on the base within a 24-hour period.
Officials also said human remains believed to belong to a third individual had been recovered and were undergoing identification.
According to the report, the first missile attack damaged the base's gym after troops had been alerted by incoming missile sirens and attempted to reach protective bunkers. Several personnel were reportedly injured while moving to the shelter.
Hours later, a second Iranian missile reportedly struck what was described as an empty aircraft hangar after another warning siren sounded.
The third attack hit containerized housing units, known as CHUs, where troops had been sleeping. Although warning sirens were activated, US officials said not all personnel were able to reach bunkers before impact.
The WSJ said the three successful missile strikes within one day underscored the difficulty of defending US military installations against Iran's ballistic missile arsenal.
US Secretary of State Marco Rubio described the incident by saying that "a missile got through," while emphasizing that most Iranian missiles had been intercepted.
The report noted that Iran has increasingly deployed high-speed, maneuverable ballistic missiles capable of complicating interception efforts, adding to the pressure on US air defense networks deployed across West Asia.
The latest details emerged as the Pentagon said nearly 100 US service members have sustained injuries in Iranian strikes since July 7, with spokesman Sean Parnell claiming most suffered minor concussions and around 96% have returned to duty.
The Jordan attack was among the deadliest recent incidents involving US forces as Iran expanded missile and drone strikes on US positions across the region, while Washington continued attacks on Iran.
Trump vowed retaliation, while Iran’s Leader Sayyed Mojtaba Khamenei warned that further US aggression would bring “unforgettable lessons.”