The 26-year-old joins The Owls for an undisclosed fee after putting pen to paper on a two-year deal with the Second Division club.
Lucas joins Guy Branston, Lee Bullen, Paul Heckingbottom and John-Paul McGovern in making moves to Hillsborough for next term.
The custodian had two loan spells with the South Yorkshire club this past season and was delighted to make his move to Wednesday a permanent arrangement.
"Everything that I hoped would be sorted out has been and I can't wait for the season to get started," Lucas told the club's official website.
"I did have my doubts that everything would fall into place but a big helping hand came from the chairman (Dave Allen) in the end.
"Chris Turner also pushed and pushed for me as well and I owe myself being here to those two people.
"The people who made me feel wanted were at Sheffield Wednesday."
