The 29-year-old has been a free agent since his deal at Bournemouth expired at the end of last season.
He spent a short time last month training with Serie B outfit Como having spoken about his lack of offers and the impact it was having on his mental health.
Now Wilshere, who played 197 games for Arsenal over 10 years, is training predominantly with the under-23s at the club’s London Colney training centre.
The PA news agency reports he will occasionally join in with the first team and use the opportunity to study coaching approaches in an agreement that will run until the end of January.
“What you should believe is that we want to help Jack prepare for his next stage, physically, mentally,” Arteta told the club’s official website.
“He wants to do his coaching badges again and we are prepared to fulfil all the needs that he wants. That is basically the idea and it is no further than that.
“I am very happy to have him back.”
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