The midfielder was out of action for four months after suffering a broken foot while on Scotland Under-21 duty.
He was an unused substitute for last week's win over Dundee and is seeking a quick return to action as the Dons prepare to face Kilmarnock in the Clydesdale Bank Premier League on Saturday
Jack said: "I'm feeling good. I did a lot of training with the physios and a lot of fitness work so I've got my fitness right back up.
"Now I'm back training with the boys so I'm feeling a lot sharper and more ready."
He added: "It was really frustrating. I'd been starting and playing in games so to go away for a friendly match and get hit with the injury wasn't ideal. But you just need to get on with it.
"It's difficult when you're not playing. You're coming in to get treatment and all the boys are training.
"But I had all my family behind me, as well as the manager and all the lads, so that made it easier coming in every day. They were all there for me and that was good.
"Now I'm back fit, I just need to concentrate on getting back in the team."
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- Clydesdale Bank Premier League