Clarke, who skippered the Seasiders and played 41 times for a club that was relegated out of the Championship, was one of 17 players who were released from Bloomfield Road at the end of the season.
The 33-year-old former Southend and Huddersfield defender has penned terms on a two-year contract at the JD Stadium.
“Peter is a very important signing for the team and the club as we enter an exciting new League One adventure,” said Shakers boss David Flitcroft.
“With his experience, knowledge and understanding of playing at higher levels, it was important to capture his services and add him to the group.
“He is a natural-born leader and organiser, a football man of stature and standing in the game. With the young, dynamic defenders we currently have at the club, he complements them superbly.
“We worked hard to secure Peter’s services as we believe he can improve and take us forward. His greatest quality is as a person.
“We already have an outstanding group of people, so it is important that we recruit good players but more importantly good people, and in Peter he possesses that great human quality that makes him stand out.”