He should now remain at the club for the rest of this season, as well as for 2016 and 2017.
The 22-year-old returns after the departure of Mickey Higham to Leigh for a £50,000 transfer fee.
“We did everything legitimately,” Wolves head coach Tony Smith said.
“We’ve paid compensation to London and rightfully so, even though he’s our player.
“We’ve found ourselves in a situation where we need him and we went through the front door and negotiated a legitimate compensation figure.
“We asked Brad if he wanted to be part of a new two-year deal with us and we’ve taken that up. He’s our second hooker for next season; he’s totally committed and that’s what we want.
“Brad has benefited from his London spell. He’s been playing week in, week out and most people at London would tell you that he’s been amongst their best performers each week.
“Brad has been part of our system and the players love him. He was outstanding against Dewsbury and Brad will get a lot of game time between now and the end of the season.”