The deal marks the club’s first acquisition since emerging from administration following its takeover by US consortium Arise Capital Partners in May.
The Owls, who were relegated to League One last season, also hold the option to extend the 31-year-old’s stay by an additional year.
Santos joined Swansea from Bolton Wanderers last summer but made only one appearance for the Championship side.
“Once I got the call from my agent telling me that Sheffield Wednesday was a possibility, I told him, make sure you get this done,” he told club media.
“There's so much I can say about the club. The support just drags players in. The fans are unbelievable, plus the manager’s energy and his ambitions.
“The club struggled last year and had its problems, but all of that is over now – as you can see by how many season tickets we’ve sold. Joining at this time, there is no better feeling for me.”