The world-class loosehead has been heavily linked with Toulon, where he would join up with the likes of Jonny Wilkinson, Matt Giteau and Bakkies Botha, but he has yet to announce his exact destination.
'I definitely will not be with the Blues next season, and yes, I am going to France,' Jenkins told the Western Mail.
'I was offered a deal by the Blues, but that was after talks were put off about an extension on several occasions.
'In the end, they said they couldn't pay me while I was fulfilling international commitments, and so I felt I had no choice. I had to think about my future, just like any player or anyone in any walk of life would do.
'I won't leave with any bitterness and I will give the Blues everything between now and the end of this season, just the same as I have always done. But after that, it will be time for me to have a fresh start and a new challenge.'
That fresh start means Jenkins will be based abroad when the Lions head to Australia in 2013.
Jenkins won Test caps in 2005 and 2009 and is a heavy favourite to be among the front-row resources when Britain and Ireland's elite take on the Wallabies the summer after next.
He joins fellow Wales and Lions stars Mike Phillips, Lee Byrne and James Hook in the Top 14, with Aled Brew, Luke Charteris and Huw Bennett also looking likely to ply their trade in France next term.