It says Tariq al-Harzi was responsible for co-ordinating suicide bombings in Iraq and moving weapons from Libya to Syria.
The US had offered a $3m (Â£1.9m) reward for the man it called the "emir of suicide bombers".
IS has not commented on the reports of his death.
Harzi was allegedly killed in the northern-eastern Syrian town of Shaddadi on 16 June.
The US Treasury Department had placed him on a sanctions list after designating Harzi as a "global terrorist".
It is thought that he had assisted foreign fighters from the UK, Albania, and Denmark.
He also raised funds for the group, including $2m from a single Qatar-based donor.
A Pentagon spokesman said Harzi's death was a blow to Islamic State.
"His death will impact [IS's] ability to integrate foreign terrorist fighters into the Syrian and Iraqi fight as well as to move people and equipment across the border between Syria and Iraq," Capt Jeff Davis said in a statement.
In June the Pentagon said it had killed Harzi's brother in a drone strike.
Ali al-Harzi was a person of interest in the investigation of the 2012 bombing of the US consulate in Benghazi in Libya. The US says he was killed in a drone strike in the IS stronghold of Mosul in northern Iraq.

The facility at Brow Top, which has a 24m pool and squash courts, had to been due to open to the public on Saturday.
However, because of "a small number of snagging and technical issues" relating to the learner pool, the opening date has been put back by a least a week.
The council's deputy leader, Mark Fryer, said the centre would not open until it was "pristine".
He said: "We can handle it being late but we can't handle it not being perfect. I wanted this facility to open as soon as possible but I wanted it to be pristine.
"There's a technical problem with the small pool and problems with drains which are not finished."

Officials said further refinement of satellite data found the plane may have turned south earlier than thought.
The announcement came as Australia and Malaysia signed an agreement on the search's next phase, which will see the two countries sharing costs.
The Beijing-bound plane disappeared on 8 March with 239 people onboard.
Based on analysis of satellite data, it is believed to have ended its journey in seas far west of the Australian city of Perth.
Investigators do not know what happened to the flight and finding its "black box" flight recorders is seen as key to understanding the factors behind its disappearance.
Australia, which is responsible for search and rescue operations, has been looking for the plane in an area about 1,800km off its west coast.
The latest detail on the plane's possible flight path came from an analysis of a failed attempted satellite phone call from Malaysia Airlines to the plane, said Australia's Deputy Prime Minister Warren Truss.
"The search area remains the same, but some of the information that we now have suggests to us that areas a little further to the south... are of particular interest and priority," he told reporters in Canberra.
A Dutch contractor, Fugro Survey, will kick off the next phase in the search in September. Three vessels towing underwater vehicles will scan for the plane.
The search will focus on an area of about 60,000 sq km and is estimated to cost about A$52m (Â£29m, $49m).
Malaysia's Transport Minister Liow Tiong Lai signed the memorandum of understanding with Mr Truss.
The two were also briefed on search efforts, together with China's Transport Vice-Minister He Jianzhong.
Most of the passengers onboard the flight were Chinese. The ministers issued a statement saying they "remain cautiously optimistic" that the plane will be found.
A senior member of the Islamic State (IS) group has been killed in an American drone strike in Syria last month, according to the US military.
[NEXT_CONCEPT]
The opening of a new £11m leisure centre in Workington has been delayed.
[NEXT_CONCEPT]
Australia says the search for the missing Malaysia Airlines flight MH370 will focus on the southern part of the search area in the Indian Ocean.