Saturday's bombing raid, the first known American assault on a top Afghan Taliban leader on Pakistani soil, marks a major blow to the militant movement, which saw a new resurgence under Mansour.
"We have removed the leader of an organisation that has continued to plot against and unleash attacks on American and Coalition forces, to wage war against the Afghan people, and align itself with extremist groups like Al-Qaeda," the US president said in a statement.
Obama, who is on a three day visit to Vietnam, said Mansour had rejected efforts "to seriously engage in peace talks and end the violence that has taken the lives of countless innocent Afghan men, women and children."
He called on the Taliban's remaining leadership to engage in peace talks as the "only real path" to ending the attritional conflict.
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Mansour was elevated to the leadership of the Taliban in July 2015 following the revelation that the group's founder Mullah Omar had died two years earlier.
It was believed to be the first time the United States has targeted a senior Taliban figure in Pakistan.
Pakistan, which says it is hosting the Afghan Taliban's top leadership in order to exert influence over them, has lambasted the United States over the drone attack, calling it a violation of its sovereignty.
In his statement, Obama said American forces would continue to go after threats on Pakistani soil.
"We will work on shared objectives with Pakistan, where terrorists that threaten all our nations must be denied safe haven," he said.
The US has carried out hundreds of drone strikes in the Pakistan, mainly in the country's border tribal regions with Afghanistan, with leaked documents showing Islamabad had quietly consented, despite publicly protesting.