After rejecting a first approach on Thursday, Boro have now agreed compensation terms with Wolves and granted Edwards to speak with the Premier League club.
Boro stood down Edwards for victory over Birmingham City and released a statement before kickoff to explain the situation.
It read: "Middlesbrough Football Club have, subject to the completion of an agreement with Wolverhampton Wanderers FC, given head coach Rob Edwards permission to speak to Wolves.
"We initially rejected an approach from Wolves on the basis that Rob signed a three-year contract with MFC less than six months ago.
"Following discussions with Rob, we were disappointed to learn that he wanted to speak with Wolves regarding their head coach vacancy. We have now agreed terms with Wolves, subject to the completion of the relevant paperwork.
"First team coaches Adi Viveash and Harry Watling, and Academy manager Craig Liddle, will take charge of team affairs for Saturday's game against Birmingham City at the Riverside."