Striker Barnes has completed a seven-match suspension imposed by the Football Association after he appeared to trip referee Nigel Miller at Bolton last month.
Poyet admits the 23-year-old would not be walking straight back into his side were it not for injuries to fellow frontmen Craig Mackail-Smith and Will Hoskins.
He told reporters: "He is very happy, excited, a different person than what he was a month ago and ready.
"When you're injured you can do nothing about it but when you are fit and training every day but can do nothing at the end of the week because you're suspended it's difficult. But it's his own mistake so there is nothing anyone can do. He is ready and he is happy to be back.
"I think he is lucky. If Macca or Hoskins were fit and playing all right, Ash would not have a chance to come back, it's as simple as that.
"I hope he uses that luck for the good of the team. That means performing and not doing anything silly.
"If he can do that and helps us we will help him like we always do. It's a two-way thing, so we'll see. If he plays he'll have a chance to help us."