"The more we have talked about it as a family, the more I have realised I joust couldn't do that again.
"If I was single or lived closer, I'd have never contemplated moving on," he said.
"Last season Matty Richards kindly let me use his spare room so without him it would've been more difficult, so I'd like to thank him for that."
Walsall boss Chris Hutchings said: "We wish Jamie all the best. He's an excellent professional and , as much as we wanted him to stay, it wouldn't have been right for player or the club to stand in his way."
Vincent signed for the Saddlers permanently in August 2009 and previously played 12 times during a loan spell from Portsmouth from December 2003 to January 2004.
"It's a great bunch of lads at Walsall and, in that sense, I'm gutted to going. However, I've got to think of what's best for my family and I'm hoping to get something sorted with a team nearer to home in the coming days," he said.
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