Wilshere will wear the number 10 jersey this season following the departure of Robin van Persie to Manchester United.
The England international is expected to return to competitive action in October after over 12 months out with injury.
"We lose great players but I want to show that we have great players at the club," said the Frenchman on Arsenal's official website. "We have young players, English players like Oxlade-Chamberlain and Wilshere. We have fantastic potential here and when everyone is fit we will see that.
"I feel Jack will be one of the leaders of this club and by giving him the number 10 shirt I want to show I am confident he will be the one who will lead the team one day. I believe that he is at the stage where he needs something at the moment. At his age after one year out, that is not easy to take.
"Every day he comes in at eight o'clock in the morning and works out but didn't get anywhere. I want to show him that I believe in him and that he will come back quickly."
Summer signing Santi Cazorla will wear the number 19 shirt now, while striker Lukas Podolski has been allocated the number nine shirt.