The 28-year-old departed Rangers last week, so as a free agent did not need to be signed before Friday's transfer deadline.
Club secretary Matt Williams told the Blackpool Gazette: "There was no rush to beat the transfer deadline with Kirk as he is a free agent.
"We spoke to him last week and everything was agreed, so it was just a case of actually getting him to Blackpool for a medical."
Boss Ian Holloway added: "We are hoping to have Broadfoot with us shortly and maybe another, someone who hasn't been mentioned as yet but a player I'm keen to get in and work on. We'll see if we can get that deal done early this week."