The Stoke City defender, who is already well-known to Wednesday fans having made 59 appearances for the club over two loan spells, emerged as a potential Owls target over the weekend, though there were said to be a number of rivals for his signature.
But the link came and went in a couple of days after Sunderland won the race to sign the 31-year-old, with his signing confirmed on an 18-month deal.
Wednesday have made no secret of their desire to add defenders to a squad torn apart by injuries in this campaign.
At stages of the season Dominic Iorfa, Chey Dunkley, Lewis Gibson and Sam Hutchinson have all had long-term issues, with Hutchinson the only available recognised centre-half at the club at current.
Iorfa is expected back in February, while Dunkley faces a number of weeks out with a hamstring issue. Gibson is back training with Everton and his Wednesday future is unknown.
The loss of Batth to a promotion rival will no doubt be seen as a blow to Wednesday, who are looking to bring two centre-halves in in the coming weeks.
Among the other defenders linked with a move to Hillsborough this month are Mark Beevers, Haydon Roberts and Stuart Findlay.
Speaking after their impressive win over Plymouth Argyle on Saturday, Owls boss Darren Moore suggested it may be difficult to add any new players to the squad before next weekend’s visit to Oxford United.