The highly-rated attacking midfielder is expected to go straight into the Bolton squad for Saturday's Premier League encounter with Liverpool at Anfield.
Bolton manager Coyle told the club's website: "Jack is a talented, young, hungry player who I think has got a bright future ahead of him.
"He has got an abundance of quality and he will enhance our squad.
"It is similar to the deal with [Manchester City loanee] Vladimir Weiss in terms of the belief that I can help the player and the player can help this football club.
"The deals suit all parties concerned if the boys go and deliver on the pitch."
Wilshere, who has represented England at all youth levels including Under-21, became Arsenal's youngest ever league player at 16 years and 256 days when he made his debut as a substitute at Blackburn in September 2008.
The Stevenage-born teenager signed a new long-term contract with Arsenal in July.
Liverpool 4/9, Draw 10/3, Bolton 6/1