Moore has done an outstanding job at Doncaster in his time in charge after replacing Grant McCann in the summer of 2019. Rovers pushed for the League One play-offs last season before the first lockdown and were in promotion contention again this season.
But the former West Brom manager has now been enticed to return to the second tier at Wednesday and has swapped a promotion fight for a relegation battle.
Moore replaces caretaker manager Neil Thompson and his first match in charge will be Wednesday's South Yorkshire derby with Rotherham United.
Meanwhile, Rovers have expressed their disappointment at the developments, while naming Andy Butler as their new manager with immediate effect.
Moore is known to have heard previous concerns about the club being able to sustain their quest to progress to the Championship, but was supported in the last transfer window after the club lost Ben Whiteman to Preston North End.
But he has now elected to make the move to Hillsborough, with the former defender understood to have been keen to return to the second-tier for some time.
Moore is set to take training at the Owls' Middlewood Road training ground today. He is the Owls' third manager of the season.
Wednesday reportedly made an approach to Rovers to speak to Moore on Friday, with Moore's representatives informing the club on Saturday morning that he wished to speak to the Owls - ahead of making a decision to take the job on Sunday night.
Rovers have received a six-figure compensation fee for Moore.
Chairman David Blunt said: “We are disappointed that Darren has chosen to leave the club part way through what has been a season full of promise.
"We have made significant efforts to support Darren over the past 18 months and ensure he was able to build a team capable of challenging in the top six. This has included supporting him through the past two transfer windows despite the difficult financial circumstances.
"Our ambitions remain to achieve a top six finish and we hope and expect that Andy will use this time to put himself in the prime position to secure the role on a permanent basis at the end of the season. Andy’s first priority will be to halt the team's recent run of poor form and put our season back on track.”
Moore's assistant Jamie Smith has also left the club with immediate effect.