The former West Ham United man verbally committed to the offer two weeks ago and signed upon his return from getting married in America.
Spector, 27, has joined Wade Elliott, Colin Doyle, Paul Robinson, Callum Reilly, Mitch Hancox and Will Packwood in penning fresh terms at St Andrew's.
Boss Lee Clark told the club's official website: "Jonathan signing is a big boost and I'm looking forward to having him back in the group and being part of the squad.
"He was the last one of three lads that were out of contract to commit to the club.
"In terms of football he's still young, but he's a very experienced player in terms of the games he's had for a player of his age.
"His versatility is a big thing for us because he can cover different positions.
"As well as midfield he can play as a full-back, although I ultimately think that as he goes on he could be a decent centre-half because he's an aggressive player, he's got good aerial ability and he's mobile."