The Broadway production, which starred Steve Kazee and Cristin Milioti, won eight Tony Awards, including best musical, in June.
The BBC said "Once" will replace the long-running "Blood Brothers" at London's Phoenix Theatre. Sandwiched in between the two productions will be a limited engagement of "Goodnight Mister Tom."
The British broadcaster said booking dates, as well as the cast and creative team for the West End version of the Broadway hit, are expected to be announced soon.
Based on a 2006 film by the same name, the musical follows an Irish busker and a Czech immigrant drawn to each other through their mutual passion for music.