The 23-year-old has joined the Owls for an undisclosed fee, believed to be in the region of £7million.
The Boro academy product departs the Riverside Stadium having made 70 appearances in all competitions for the Teessiders.
#DeadlineDay | @AdamReach has completed his move from @Boro to #swfc. Read the full story at https://t.co/Ofdb166N9kpic.twitter.com/rraaKavjnI
— Sheffield Wednesday (@swfc) August 31, 2016