The 28-year-old agreed to stay with the Glasgow giants despite their demotion to the Third Division but was since allowed to the leave the club.
Broadfoot had already made five appearances for Ally McCoist's side this term, helping them to third in the table, two points behind leaders Peterhead.
"It's a new chapter to my career and one I'm looking forward to. Something I've always wanted to do is play down south," he told BBC Radio Lancashire.
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|7/1||Blackpool are 7/1 with William Hill to be win the Championship|
"It's a sad day [to leave Rangers] because it was always a dream to play with them.
"I almost signed here a couple of seasons ago and I stayed with Rangers at that time, but speaking to the manager, I was blown away by him and the way Blackpool play.
"I've watched them a few times since then and my friend, Charlie Adam, played here. People couldn't speak highly enough of the club.
"Blackpool has got something special about it. It seems to have this aura about it. Everyone seems to enjoy themselves here."The versatile defender joined the Gers in 2007 and established himself as a regular started under then-manager Walter Smith, before a series of injuries hampered his progress.
Blackpool are currently top of the Championship with nine points from their opening four games.