The England U21 international joins the Rams on loan until the end of the season and will be in line for a debut in Saturday's home game against Birmingham City.
Wisdom, who can play either at centre-back or right-back, turned out 19 times for Liverpool last season but only three times this term.
Former England manager McClaren was keen to strengthen Derby's leaky defence which has failed to keep a clean sheet in the last nine fixtures and let in 20 goals in 12 games league games.
"Andre is a very good and a promising player who we're delighted to welcome to Derby County," McClaren told the club's website.
"Liverpool obviously think a lot of him but he's at the stage of his development where he needs to play some first-team games, and we're delighted they see Derby as the place to do that.
"We've had a few injuries in defence of late and Andre will bring extra qualities as well as more competition for places, which is always welcome."
Wisdom is the second signing at Pride Park in the space of a week following striker Simon Dawkins' arrival from Tottenham on a three-month deal.