"Stay with Me", penned by Jerome Moross and Carolyn Leigh, was recorded by the Rat Pack legend in 1964 and appeared the following year on his compilation album Sinatra '65: The Singer Today.
Dylan's version is available on stream right now.
The song will appear on the 73-year-old's all-Sinatra covers album Shadows in the Night, which is due on February 3. The LP was hinted as early as last May, when Dylan released album artwork and a cover of another Sinatra favorite, "Full Moon And Empty Arms".