Wilshere has struggled with injuries in recent campaigns but on Thursday headed off to the Asia with the rest of Gunners' squad for their pre-season tour.
And Oxlade-Chamberlain believes 21-year-old Wilshere will play a key part during the forthcoming season.
He said: "Jack is back in training and looking really good. He is coming away with us on tour and the fact he is looking so strong is good news for Arsenal and England.
"Hopefully, he can stay fit because he is an amazing player and can add a lot to our team. He is the best kind of signing we can make.
"Whenever you lose someone it dents the team in some way. If we can keep him fit, it will give us a lot more options and enhances competition for places.
"He is a much stronger character now, on and off the pitch.
"He works really hard and is the first one in and last one out of training. Having not been able to play for so many months is really mentally challenging but he did that really well.
"Last season he had a good stint in the team and now he is pushing on again."