Appleby had his contract paid off last December after Molby's replacement Peter Taylor lost patience with the player's constant unavailability.
However, Molby - who has previously managed the 28-year-old at Swansea, Kidderminster and City - believes he can get the best out of him back at Aggborough, and has secured his services on a non-contract basis.
Harriers boss Molby told their official website: "By registering him as a non-contract player it means he can now play for us if we want him to.
"Richie has been working very hard over the past ten weeks but he knows he still has a long way to go. We have seen that he still has the ability to become the player he once was, the only question is can his body cope?
"I'd like to think that is possible, it's now up to Richie to prove that."
Elsewhere, another product of Molby's failed spell as Hull City manager, Shaun Smith, has signed for Conference side York City.