The versatile 33-year-old can play at right-back, central defence, central midfield and has even had spells in attack during his long and illustrious career.
The former Newcastle, Aston Villa and Everton player left The Baggies on a free transfer and signed a two-year deal at Hillsborough which will be completed on Thursday after Watson passed a club medical.
Watson joins Richard Hinds, Lee Grant and Robert Burch at S6 this season with Brian Laws wanting to more firepower to his squad before the start of the season.
The player was excellent at Hillsborough last season when Laws brought him in on loan and helped Wednesday in their late push for the play-offs.
Meanwhile, former Birmingham winger Julian Gray, who was linked with a move to The Owls yesterday, has joined Coventry City.