He was killed after US special forces raided a remote mountainous cave complex hoping to capture him.
“Al-Sudani was responsible for fostering the growing presence of ISIS in Africa,” Defence Secretary Lloyd Austin said.
He also allegedly funded the group’s activities globally, Mr Austin added.
Analysts say the fact that US troops were sent under orders of President Joe Bidento kill or capture Sudani, rather than using a less risky drone strike, indicates his significance.
Details about the nature of the operation have not been released, however the soldiers were drafted in via helicopter, according to the New York Times with Sudani killed after a gunfight broke out.
The operation comes after President Biden redeployed hundreds of US troops to the country after his predecessor, Donald Trump, pulled them out. However, those forces are reportedly only there to train Somali soldiers, rather than conduct operations.
In recent years, the Islamic State group has reportedly expanded its activities into several African countries, including Mozambique and the Democratic Republic of Congo.
However Islamic State is a relatively small group in Somalia, with the al-Qaeda linked group al-Shabab far more prominent – it controls many southern areas.
Prior to joining Islamic State, Sudani allegedly did operational work for al-Shabab, assisting with training fighters.
He is accused of playing a “financial role with specialized skills which made him an important target for US counterterrorism action,” an anonymous US official told the AFP news agency.
The operation to target Sudani is said to have taken months to plan.
Somalia has welcomed the killing of Sudani, according to the Voice of America news site.
“It’s a very positive and welcoming,” said Somali government security adviser Hussein Sheikh Ali.
He stressed that Islamic State was not as big a threat as al-Shabab in Somalia, but that Sudani was “dangerous”.
“The message is, that the leaders of all terror groups in Somalia are not safe,” he continued.
IS Somalia is one of the group’s smaller branches – claiming 32 attacks in 2022, mostly in the capital of Mogadishu.
One UN report from last year estimated the number of Islamic State fighters in Somalia was around 200 to 280 and that the country is used as a significant base to finance IS activity in Iraq and the Levant, but this has not been independently verified by the BBC.
Just last week IS published a rare propaganda video from its Somalia branch, which showed combat footage of clashes with Somali forces in a mountainous region in the north-eastern Bari region.
The raid comes less than a week after the US said a drone strike had killed 30 al-Shabab militants.
In recent months, pro-government forces in Somalia have been making progress against al-Shabab.