Wisdom's switch to the Championship side was agreed last month but the club waited until the player returned from his summer holiday, following the successful completion of a medical.
"I loved it at Derby so it is good to sign," he told the official Derby website. "It helps that I have been here before so I am familiar with some of the players and staff, as well as how the club works, so it made the decision easy.
"To be honest, Derby does feel like home. When I was here before we had a great season and we were unlucky at the end not to go up, but aside from the play-off final everything clicked and we all enjoyed it.
"I feel that I played the best season of my professional career here before. Even after I left Derby and went elsewhere, I don't think I was playing the kind of football that I was during that loan spell. It's good to be back and I hope I can replicate what I did before this time around."
Wisdom, who made 22 first-team appearances for Liverpool, helped Derby reach the Championship playoff final in 2014, losing to Queens Park Rangers.