The couple's duet appears on "Bolton Swings Sinatra," which hits U.S. stores May 23, People magazine reported Monday.
Bolton, 52, and Sheridan, 42, were together for six years in the 1990s. They remained friends after breaking up, rekindled their relationship last year and announced their engagement last month.
"The second time around is a big deal for us," Bolton, who is currently touring, told People from South Korea.
Bolton said Sheridan helped him pick the Sinatra songs for the new album.
The "Desperate Housewives" star was a little intimidated as they headed into the Capital Records studio to record "The Second Time Around," he said.