The 30-year-old had been without a club since leaving Bournemouth last summer and had spent time training with Italian Serie B side Como and former club Arsenal.
Once touted as a future England star, Wilshere has been plagued by injuries throughout his career, making just 19 appearances in two years at West Ham United after leaving Arsenal in 2018.
"Since I started training with Arsenal, I have never hidden that it was to be ready for 2022 and for a new club," Wilshere told the club's website.
"It has now succeeded and it will be an exciting new challenge for me. I am at a point in my career where I need to get started again after a difficult period, and that opportunity AGF has offered me.
"I am very grateful for that and I will do everything I can to help the team move forward.
"I have been looking for a change of air and a fresh start in a new framework, and I am very much looking forward to contributing to the team.
"It's clear that I lack a bit of training, but I'm physically in really good shape and fit, so now it's about me to get well into the squad and see if I can earn playing time for the club and contribute to , that we can get some points on the account."
Aarhus are currently seventh in the Danish league.
