Born and raised in Madrid Corella trained with Karemia Moreno and Victor Ullate and began winning dance awards at a young age.
When the world-renowned, Russian ballerina Natalia Makarova, saw the young Corella in competition, she contacted the artistic director of American Ballet Theatre and recommended that he be auditioned for the company. He was accepted into ABT as a soloist in April 1995 and was promoted the following year (August 1996) to the rank of principal dancer. Ángel Corella has performed as a guest artist with such companies as The Royal Ballet in London, the La Scala Ballet in Milan, the New York City Ballet, the Australian Ballet, the Ballet of Tokyo, the Asami Maki Ballet, Ballet Contemporaneo de Caracas, and the National Ballet of Chile. In March 2008, Corella made his debut with the Kirov Ballet at the Mariyinsky Theatre in St. Petersburg, Russia, dancing the role of Prince Siegfried in Swan Lake.
Corella has also performed in all the most prestigious festivals, galas, and special performances around the world, including The Kings of the Dance which premiered, in February 2006 at NY City Center. In 2007, Kings of the Dance toured to Russia with performances in St. Petersburg, Moscow, and Perm, Russia. The next year, Angel Corella was the sole returning original cast member to perform it at the Mariinsky Festival. Prior to 2008, he toured Spain extensively with his own company Ángel Corella & Stars of the American Ballet.
In recent years, Corella has danced for Elizabeth II of the United Kingdom and the President of the United States. He has performed all of the classics and has received critical acclaim for his technique, musicality, and for his sensitive, dramatic interpretations of roles in ballets by Sir Kenneth MacMillan, specifically Romeo and Juliet and more recently, Manon. He has had the opportunity to partner many well-known ballerinas including Alessandra Ferri, Xiomara Reyes, Julie Kent, Gillian Murphy, Diana Vishneva, Alina Cojocaru, Nina Ananiashvili, Paloma Herrera, Irina Dvorovenko, Viktoria Tereshkina, Alina Somova, Evgenia Obraztsova, Alexandra Ansanelli, Michele Wiles, Stella Abrera and Letizia Giuliani, among others.
His appearances on television and film include:
- 2000 PBS presentation of documentary film Born To Be Wild - The Leading Men Of American Ballet Theatre
- 2005 (Emmy Award-winning) PBS presentation of Tchaikovsky's Swan Lake, with Gillian Murphy and Marcelo Gomes (Staging by Kevin McKenzie
- Swan Lake with Gillian Murphy (American Ballet Theatre - 2005)
- Romeo and Juliet with Alessandra Ferri (La Scala Ballet - 2000)
- Le Corsaire with Julie Kent/Ethan Stiefel (American Ballet Theatre - 1998 VHS, 2001 DVD)
- Born To Be Wild - The Leading Men Of American Ballet Theatre (Biographical Documentary - 1999) with Vladimir Malakhov, Jose Manuel Carreño, and Ethan Stiefel.
- Don Quixote Pas de Deux with Paloma Herrera (American Ballet Theatre) on a mixed bill DVD titled American Ballet Theatre Now - Variety and Virtuosity (1996)
- National Ballet Competition of Spain - First prize, May 1991
- Concours International de Danse de Paris - Grand Prix / Gold Medal, December 1994
- Prix Benois de la Danse, 2000
- National Award of Spain, 2003
- Dance Europe Magazine DANCER OF THE YEAR Award, 2007
- Leonid Massine Award, 2008
- International Medal of Arts, Madrid, Spain, 2009
In April 2008, Corella established the first classical ballet company in Spain in 20 years, the Corella Ballet, Castilla y Leon; in February 2012, it moved to Barcelona and became the Barcelona Ballet.
In 2013 Corella started his own ballet school in Barcelona.