The deal struck by the full-service independent music publisher, which has offices in New York and Los Angeles, also takes in name, image, likeness and life rights for Holiday who passed away in 1959 aged 44.
Bicycle's co-president Steven Salm said: "Billie Holiday is a one-of-kind and Bicycle is committed to bringing the appropriate opportunities to her collective body of work around the world."
Holiday stands as one of the giants of jazz both as a recording artist and songwriter with her compositions including Lady Sings The Blues, God Bless The Child and Fine And Mellow. Her controversial 1939 recording Strange Fruit was named by Time magazine in 1999 as the song of the century.
She won 10 Grammy awards, including a posthumous lifetime achievement award in 1987, while was she inducted into the Rock 'n' Roll Hall of Fame in 2000. She is the subject of U2's hit Angel Of Harlem, which featured on their 1988 album and movie documentary Rattle & Hum.
"Ms Holiday's body of work, her voice and her image are simply magical. She will forever be an essential part of American culture," said Bicycle CEO Roger Miller. "That her heirs have chosen to pass the torch to us as the keepers of her legacy is an honour."
Bicycle was founded in 1974 and now owns or administers copyrights by such talents as Marvin Hamlisch, Glen Ballard, Nine Inch Nails, Jefferson Airplane/Jefferson Starship, Tammy Wynette and Cyndi Lauper.