The former Tottenham and Hull centre-back, capped once by England in a 2004 friendly against Sweden, spent the past two seasons at Selhurst Park where he was out of contract.
"This is a great move for me," said Gardner.
"I am really impressed with the ambition of the manager and the chairman and, as everyone knows, Sheffield Wednesday have a huge fan base.
"The club has the ambition and the drive to succeed and that is what has attracted me to Hillsborough."
He added: "I have played a lot of my career in the Premiership and that is where I want to return to.
"I have no intention of coming to a club that is just out to consolidate in the Championship. I want to succeed and that is why I have come to Sheffield Wednesday."
Owls boss Dave Jones added: "I am really pleased to bring a player of Anthony's calibre to the club. It has taken a little longer than anticipated because of circumstances - he was away while I was away and vice versa but I kept in contact with him throughout that time.
"He gave me his word and he stuck to it. Anthony is a quality player and a leader, with Championship and Premiership pedigree. He will help take Sheffield Wednesday forward."
