The actor collaborated on the project with producer T-Bone Burnett, who won an Oscar himself for co-writing the "Crazy Heart" song "The Weary Kind."
Bridges wrote some of the material and also covered compositions by the likes of Tom Waits and late "Crazy Heart" songwriter Stephen Bruton. Guest vocalists on the album include Rosanne Cash and Burnett's ex-wife Sam Phillips.
A statement for Blue Note, a jazz specialist owned by EMI Group, did not disclose the album's title or the names of any songs. A spokesman did not reply to a request for more information.
Burnett, friends with Bridges for more than 30 years, also compiled the soundtrack for the 1998 film "The Big Lebowski," in which Bridges played his iconic slacker role "The Dude."
Bridges previously released an album in 2000, called "Be Here Soon," collaborating on the independent project with Michael McDonald.