Wilshere rejoined the Cherries in January and played 17 times for the club, scoring twice. Bournemouth reached the play-offs after finishing sixth, but were beaten by Brentford.
"A class act on and off the pitch," Bournemouth said on Thursday. "We'd like to thank Jack Wilshere for his efforts since returning to the club and wish him all the best moving forward."
On Wednesday, the 29-year-old Wilshere took to Instagram and said he didn't know if his future remained with the south coast side.
"Thank you to everyone at Bournemouth for the last five months," Wilshere said. "My teammates, all the staff and especially the fans. You were amazing last time and continued to support me this time.
"Being honest, I don't know if this is the end. The coming weeks will tell. Unfortunately we didn't reach our goal of promotion but there is plenty of positives and experience to take into next year to get this club back where it belongs!"
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