Earlier this week, reports suggested that Luton Town - where Caulker has been training - and teams from Turkey and China were all interested in the centre-back.
However, Caulker has opted to pen an 18-month deal with the Scottish Premiership side and the former Cardiff City and Queens Park Rangers man has admitted that he is keen to get back to playing football after his well-documented personal problems.
The 26-year-old told the club's official website: "I met Neil McCann the night before and sat down to chat with him for about an hour. I just felt that he could offer me what I need and what I want. What I want is to be back enjoying my football in a good environment with a manager who is understanding, and one who is caring and respectful.
"I feel that I've found that in Neil. I came up last night (Wednesday) and signed today. I'm excited and looking forward to getting started."
Dundee currently sit in ninth place in the top-flight standings.