Kenneth Greve studied at the Ballet School of the Royal Danish Ballet, and at the School of American Ballet. He has been a dancer with the New York City Ballet, the American Ballet Theatre, the Paris Opera Ballet (where he earned the distinction of danseur Étoile), Royal Ballet Flanders, the Stuttgart Ballet and the Vienna State Opera Ballet. He joined the Royal Danish Ballet from 1992 to 2008. He also acted as Ballet instructor in the Royal Danish Ballet from 2006 to 2008.
He has created full length choreographies such as Hamlet for South African Ballet, Nutcracker for The Royal Danish Ballet and Swan Lake for Czech National Ballet, Poznan and Finnish National Ballet. Scheherazade, The Snow Queen and The Little Mermaid for the Finnish National Ballet were premiered during his term as Director 2008-2018.
Kenneth Greve has visited several ballet companies abroad and as a guest dancer he has appeared in numerous galas and as jury member in several Ballet competitions. He has been the Chairman of the jury at the Helsinki International Ballet Competition 2009, 2012 and 2016.
Greve took up the position of Artistic Director of the Finnish National Ballet in 2008 and has announced his ending of contract in 2018.