The 35-year-old leaves Town after four years at the club.
The midfielder made more than 150 appearances during his time at the Blues.
Weston’s contract expires this summer and Chesterfield have chosen not to renew it so he will become a free agent.
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‘Westy’ played a big part in the Spireites’ run to the play-offs in the last two seasons and scored some crucial goals to help them avoid relegation in 2020.
As well as his whole-hearted performances on the pitch, the central midfielder was generous with his time off it by helping out with many community projects.
More similar announcements are expected in the coming days as manager Paul Cook meets with players today to discuss their futures.
“After four years my time at Chesterfield has come to an end,” he posted on Instagram on Monday afternoon.
"I’ve met some great people and made some very good friends.
"A huge thank you to everyone at the club for looking after me.
"I wish the club all the success in the future and I hope they can get back into the Football League where they belong.”