Biden said the death of Abu Ibrahim al-Hashimi al-Qurayshi had "removed a major terrorist threat to the world".
Qurayshi detonated a bomb that killed himself and members of his own family "in a final act of desperate cowardice", the president added.
Syrian first responders said they found the bodies of 13 people after the raid.
The operation targeted a two-storey residential building on the outskirts of the opposition-held town of Atmeh, which is in northern Idlib province and is close to the border with Turkey.
The region is a stronghold of jihadist groups that are fierce rivals of IS, as well as Turkish-backed rebel factions fighting the Syrian government.
President Biden was first briefed by US military commanders more than a month ago on the operation to capture or kill Qurayshi, a veteran Iraqi militant also known as Abdullah Qardash and Hajji Abdullah, US officials said.
Intelligence reports had established that Qurayshi was living with his family on the second floor of the residential building in Atmeh and that he never ventured outside, instead using couriers to despatch his orders to IS cells in Syria and elsewhere, they said. Another family not believed to be connected to IS or aware of Qurayshi's presence lived on the ground floor.
Biden ruled out an air strike to minimise civilian casualties and gave a final go-ahead for the special forces raid on Tuesday, monitoring it in real time from the White House situation room as multiple helicopters arrived in Atmeh around midnight on Thursday.