The majority of the music on this soundtrack, which is entirely instrumental, was composed by Alexandre Desplat. The French composer also contributed to Anderson's The Fantastic Mr. Fox and Moonrise Kingdom. He has earned six Academy Award and five GRAMMY nominations for his previous work. Also utilized are some Russian folk songs, as performed by the Osipov State Russian Folk Orchestra.

The soundtrack, currently streaming here, is being released by ABKCO Records, as were Anderson's past two soundtracks. An interesting pairing with the label was set up by former Rolling Stones' manager Allen Klein, who took control of the band's pre-1971 catalog (and era Anderson very much enjoys utilizing for his films) through hostile means. Bringing the story full circle, Klein's parents were immigrants from Budapest, Hungary - a side note that likely did not influence Anderson's film.