Owls manager Brian Laws said: "I'd like to thank Richard Wood for his long service to this football club. Richard is a very good defender at Championship level and it's no secret that we tried very hard to keep him here by offering a long-term contract.
"Unfortunately Richard did not want to accept the terms we offered him and therefore we wish him all the best for his future career.
"The deal we have agreed with Coventry means that, while we could have commanded a greater fee if we had been given this position from Richard and his agent in the summer transfer window, we have secured some return for the club as opposed to the zero return we would have received when his contract runs out next summer."
Wood, a product of the Owls' academy, recently turned down Wednesday's new contract offer, while Coventry had a bid for the Wakefield-born defender turned down last season. He made 189 first-team appearances, scoring eight goals, after making his debut as a 17-year-old in April 2003.
Coventry boss Chris Coleman, who had an offer for Wakefield-born Wood turned down last season, said: "Richard has been a long-term target for the club and we are pleased to have him here.
"This is an area of the team that I've wanted to strengthen and this is a great addition to the squad in the short-term and we will look to make it permanent in January."
Coventry defenders Ben Turner, James McPake, Marcus Hall, Elliott Ward, Stephen Wright and Martin Cranie have all been sidelined in recent weeks and Wood is expected to go straight into Coleman's squad for Saturday's home clash with Crystal Palace.