The international's decision came following the dispute between the Welsh Rugby Union and the four Welsh regions.
In a letter published by the South Wales Evening Post, Jones said: "I haven't been getting any money, but I was just hoping that the row that has blighted Welsh rugby for so long could be finally settled and I could pull on the black shirt again.
"Then on Sunday morning I received a call from the Blues asking whether I fancied a move there. I had to think long and hard about their proposal because I know all about regional rivalry and how much it matters in Wales, but my circumstances were such that I didn't feel I could turn Cardiff down."
Jones has been training with boyhood club Neath.