The Pentagon confirmed that Ahmed Abdi Godane perished in the raid on Monday in which US drones and manned aircraft rained Hellfire missiles and laser-guided bombs on a gathering of Shebab commanders.
Godane had boasted that Shebab was behind the siege at the Westgate shopping mall in Nairobi last year, which killed at least 67 shoppers, staff and security personnel.
President Barack Obama, speaking in Wales after the NATO summit, seized on the results of a Pentagon probe into Monday's raid to give definition to his separate effort to combat another radical Muslim extremist group, Islamic State (IS), following days of criticism over his anti-terror strategy.
"We are going to degrade and ultimately defeat (IS), the same way that we have gone after Al-Qaeda, the same way we have gone after the Al-Qaeda affiliate in Somalia," Obama said.
"We released today the fact that we have killed the leader of al-Shebab in Somalia and have consistently worked to degrade their operations."
Obama has been under fire for admitting last week he did not yet have a strategy to combat IS in Syria and in imprecise language since had vowed to eliminate or manage the group - before finally settling Friday on the phrase "degrade and defeat."
The killing of Godane allowed the president to fold the fight against Islamic State into what the White House says is a successful and wider strategy to combat radical Islamic extremism, which has included efforts to take out leaders of radical groups.
The Pentagon had previously announced the raid in Somalia but had been unable to confirm that Godane had been killed before Friday.
Somalia's President Hassan Sheikh Mohamud thanked the United States, and called on Shebab fighters to lay down their weapons.
He also offered Shebab fighters a 45-day amnesty, calling on them to lay down their arms and renounce ties with Al-Qaeda.
"One of the main pillars of the Somali war has gone, so there is no reason for Somalia's youth to continue with a war when its days are numbered," he said.
Shebab have refused to confirm or deny their leader's death.
White House spokesman Josh Earnest said Godane's demise represented "a major symbolic and operational loss to the largest Al-Qaeda affiliate in Africa and reflects years of painstaking work by our intelligence, military and law enforcement professionals."
US officials did not specify how Godane's death was confirmed, but in similar cases in the past, US intelligence agencies have tested DNA samples and also used information gleaned from eavesdropping.
The State Department had listed Godane as one of the world's eight top terror fugitives and analysts say his death marks a crippling setback for Shebab forces.
Godane, 37, who reportedly trained in Afghanistan with the Taliban, took over the leadership of the group in 2008 after then chief Adan Hashi Ayro was killed by a US missile strike.
