The 30-year-old, who joined the Shakers in 2006, has had his contract terminated by mutual consent and penned a two-year deal with the Welsh club where he had a loan spell last season.
Bishop leaves Gigg Lane having scored 83 goals in 264 appearances, despite serious injury problems, and goes with the club's best wishes.
A statement read: "Andy leaves with the club's blessing, and appreciation for the effort and commitment that he has shown the Shakers over the last seven seasons."
Bishop added: "Now my move to Wrexham has been completed, I'd like to thank the manager (Kevin Blackwell), his coaching staff and especially physio Tom Walsh for all their help and support over the years.
"There have been plenty of ups and downs during my time at Bury, but I've never regretted one minute of my time here.
"I've enjoyed every second of the last seven years and will remember everything about the place with great fondness.
"After all the disappointment of last season, I am really pleased that the club has a future and is moving forward at what seems to be a very fast rate of knots.
"I wish everyone all the very best wishes for the future, and a successful season for the Shakers."