An air strike by a US-led coalition killed DAESH's chief military leader in Iraq last week, the Pentagon said on Monday.
The strike hit Abu Wahib's vehicle near the town of Rutba.
DAESH terror organisation seized large portions of Anbar province in 2014, though Iraqi security forces have since last year succeeded in winning back some towns there, including Ramadi and Hit.
The death of Abu Wahib, given his senior role in military planning in Anbar, will impede DAESH's ability to conduct operations in the western province.
"ISIL [DAESH] leadership has been hit hard by coalition efforts and this is another example of that," Cook said. "It is dangerous to be an ISIL [DAESH] leader in Iraq and Syria these days, and for good reason."
The Pentagon confirmed that Abu Wahib was a former member of Al Qaeda in Iraq.
The US military and allies have been conducting air strikes in Syria and Iraq since 2014 targeting DAESH leaders and infrastructure in an effort to defeat the group.
Iraqi media have in the past year published reports of Abu Wahib's death, though the Pentagon had never confirmed his death before.
Though US-led air strikes have succeeded in taking out DAESH members and some important leaders, the group is far from defeated.
The group still controls much of its border-spanning "caliphate," has inspired global affiliates and is able to orchestrate deadly external attacks like those that killed 32 people in Brussels on March 22.
DAESH also continues to carry out suicide attacks inside Iraqi and Syrian territories that has caused the death of dozens.
Car bomb kills at least 16
A car bomb claimed by DAESH in the eastern Iraqi city of Baquba killed at least 16 people on Monday and wounded 54 others near a bakery close to the city centre.
The Amaq news agency, which supports DAESH, said a suicide bomber had targeted Shiite militia fighters in the provincial capital of Diyala, an area bordering Iran.
The sources said many of the fatalities were children eating at a nearby restaurant.
Iraqi officials declared victory over DAESH in Diyala more than a year ago, after security forces and Shiite militias drove them out of towns and villages there.
But the insurgents have remained active and militia elements have been accused of abuses against Sunni residents.