And Adkins, who previously guided League of Wales side Bangor City to UEFA Cup qualification, will take over first-team affairs while the club's board consider who will replace Laws permanently.
"Brian and Russ leave with our thanks for what they have achieved during their time with Scunthorpe United, and we wish them every success in their new appointments with Sheffield Wednesday," read a statement from SUFC.
"We are obviously very sorry to lose Brian and Russ at a time when the team are riding high in League One - but we felt that it was right to give Brian the opportunity to talk to Sheffield Wednesday, because it is a club with such huge potential and offers him the opportunity to further his career.
“Nigel Adkins will assume immediate control of the first team, and Tony Daws will take control of the reserve team. Nigel will be assisted by Andy Crosby and Ian Baraclough.
“The board are currently considering the longer-term position regarding the management structure at the club.”