US officials reported that El Shafee Elsheikh was thought to be part of the terrorist organisation's brutal executions gang known as "the Beatles".
Fellow cell member Alexanda Kotey was also captured with Elsheikh last month.
Their capture was first reported by the New York Times, who reported that American officials had wanted to keep the news secret.
Along with Mohammed Emwazi - the killer nicknamed Jihadi John - and Aine Davis, they are thought to have been part of the group named after the famous '60s band because of their English accents.
The four Londoners were linked to a string of hostage murders in Iraq and Syria during the bloody Islamist uprising.
Bethany Haines, whose father David was killed in 2014 after being held captive for 18 months, said she hoped the pair's detention could bring some closure for relatives of those murdered.
She told ITV's Good Morning Britain: "I got a call late last night to say that they had been captured and the first thought was relief, finally to know that the people that were involved in my dad's murder have been caught and will sort of serve some justice."
Asked what she would like to see happen now, she replied: "In my opinion, they shouldn't be breathing but that's not really a realistic kind of expectation. I think that they should be locked up with the key thrown away and never to be released."
It is understood that Kotey and Elsheikh have been stripped of their British citizenship, but the Home Office says it cannot comment on individual cases.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.