Ledley left Cardiff City for the Hoops on a Bosman after courting interest from Premier League clubs, including Stoke.
Derby County veteran midfielder and TV pundit Savage told the Sunday Mail: "I've watched Joe for Wales and he's technically very good. He's got a great left foot and scored goals galore for Cardiff at one stage.
"Lenny will get the best out of him. He certainly got the best out of me when we were at Leicester.
"As a player, Neil inspired others around him - he used to give me some rollickings. So I can only imagine what he'd be like as a manager.
"He's a winner and I'm sure he'll get Joe playing well up there.
"He's one of Wales' big hopes along with Ramsey and Collison - we all want to see him doing well especially with the Euro qualifiers against England ahead.
"You don't just become a bad player overnight. If he continues to work hard he'll show how good a player he is.
"Joe will have had his own reasons for going to Scotland in the summer.
"Everyone's different. No-one would argue that Celtic are bigger than Stoke - but in terms of footballing ambition, it's probably a sideways step for Joe.
"Stoke are 10th in the Premiership right now, whereas he's gone to a league where he isn't testing himself every week. You just don't do that in the SPL."