Wilshere saw his progress last season hampered by a series of niggling injuries, which eventually required minor surgery, but has been tackling pre-season head on and he jetted off with the rest of the Gunners squad for their tour to Asia on Thursday.
Arsenal have already recruited France Under-21 attacker Yaya Sanogo on a free transfer and have been linked with big-money moves for Real Madrid's £25million-rated forward Gonzalo Higuain, Liverpool's Luis Suarez and Everton midfielder Marouane Fellaini, as well as Manchester United forward Wayne Rooney.
Oxlade-Chamberlain, however, feels 21-year-old Wilshere can help drive the Gunners on with his all-action displays at the heart of the team.
"Jack is back in training and looking really good. He is obviously coming away with us on tour today and the fact he is looking so strong is good news for Arsenal and England," Oxlade-Chamberlain said in the London Evening Standard.
"Hopefully, he can stay fit because he is an amazing player and can add a lot to our team. Is he the best kind of signing we can make? Yes.
"Everyone is important. 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."
Wilshere has shown great personal strength to return from almost 18 months on the sidelines a couple of seasons ago, and is now very much an integral part for both club and country ahead of next summer's World Cup.
"One thing I have realised as he's gone through this, he is a much stronger character on and off the pitch. He has learned from it and has become a better man for it. He does a lot of stuff now to prevent these things from happening," added Oxlade-Chamberlain, who scored in England's 2-2 draw against Brazil at the Maracana last month.
"He works really hard and is the first one in and last one out of training. To come through something like that, having not been able to play for so many months and always stay positive, 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."
Arsenal's pursuit of Higuain continues to drag on, with Madrid president Florentino Perez claiming no official bid had been lodged. It has also been reported the striker is now set for talks with new manager Carlo Ancelotti about whether he in fact has a future at the Spanish giants when pre-season training resumes next week.
While in the Far East, Wenger's squad will take part in a lucrative promotional tour, which includes open training sessions as well as matches in Indonesia, Vietnam and Japan.