H‹bbe was born in Copenhagen and began his training in 1978 at the Royal Danish Theater Ballet School. He was appointed a principal dancer at the Royal Danish Ballet in 1988, where he danced roles ranging from romantic leads in Romeo and Juliet and August Bournonville's La Sylphide to works by George Balanchine.

He joined NYCB in 1992 and the School of American Ballet's faculty in September 2005.

The Times quotes Mad Ovlisen, chairman of the board of the Royal Danish Ballet, as saying, "Nikolaj H‹bbe is an obvious choice as artistic director."