The former Magpies skipper leaves the club after four years at Meadow Lane, during which time he helped Notts lift the League Two title.
Bishop made 186 starts and scored 12 goals during his stay, including a famous FA Cup fourth-round header against Manchester City which earned the club a replay and a trip to the City of Manchester Stadium.
The 31-year-old's most prolific campaign was last season when he scored seven times.
On his departure, Bishop said: "It's an emotional day. This club has been a major part of my life for four years and I can honestly say I wouldn't change a thing about my time here. It's been the best part of my career.
"The club are heading in a different direction and there are a number of changes this summer and it just seemed the right time.
"I've had meetings with the manager and the board and I've given my reasons and I'm really grateful to (chief executive) Jim Rodwell, who has been very understanding and helped me.
"It's been fantastic. From the rollercoaster of the first season, the cup runs, captaining the club at Juventus and leading the lads out everytime, representing the club was a massive honour. It's probably my proudest moment in my life.
"The fans have been absolutely fantastic with me. I'd like to wish them all the best and thank them. I can't speak highly of them."
The club added in a statement: "Everyone at Meadow Lane would like to wish Neal all the very best at his next club and thank him for his service at Notts."