The 33-year-old said he "couldn't wait forever" for his playing future to be resolved, in a letter published by the South Wales Evening Post.
British and Irish Lions Test tighthead Jones has been out of work since his Ospreys contract expired at the end of last season.
He has been training with his former club Neath, as any prospective new deal with the Ospreys hinged on a solution being found to the long-running and ongoing dispute over a fresh agreement between the Welsh Rugby Union and Wales' four professional regions - Ospreys, Blues, Scarlets and Newport Gwent Dragons.
"A s pretty much the whole world and his wife will know by now, I had been waiting for a deal to be struck between the regions and the Welsh Rugby Union over a new participation agreement so the Ospreys could conclude a fresh contract with me," he 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. I haven't been paid for two months and the season is barely a fortnight away. I need to be properly attached to a team and training with a group of players in readiness for the new campaign.
"I couldn't wait forever. The contract with the Ospreys has been on the table since January, but without signatures it meant only so much.
"No-one is to blame. Andrew Hore (Ospreys chief executive) and Steve Tandy (head coach) have been straight down the line with me throughout the negotiations. They haven't messed me about and I don't think I have messed anyone about, either."
Jones, meanwhile, predicted a bright future for the Ospreys.
"T hey are going through a rebuilding phase, but with someone like Alun-Wyn (Jones) there - an immense presence in every respect - I still expect them to be pushing for a play-off place in the PRO12," he added.
"There are also a lot of young players at the region who are going to make Welsh rugby sit up and take notice in the years ahead.
"But a new chapter starts for me now, and I'm just glad I'll be able to focus on rugby again.
" Every player goes through bad times as well as good during his career, and the brilliant thing about Ospreys' supporters is that they have always been there for me when things haven't been going as well as I might have wanted.
"I will appreciate that for the rest of my career and beyond. It has been quality all the way."