Corella joined the American Ballet Theatre as a Soloist in April, 1995 and in August 1996, was promoted to Principal Dancer. Corella has also been a guest star with The Royal Ballet (Great Britan), Australian Ballet, la Scala Ballet, Asami Maki Ballet Tokio, Ballet of Chile, The Hungarian National Ballet, Ballet of Georgia, Finland Ballet, Puerto Rico Ballet, Bolshoi Ballet, New York City Ballet and Kirov Ballet of Sant Petersburg.

Angel Corella's repertoire includes all the principal roles of the leading classical, neoclassical and contemporary ballets. Classical: Basilio in Don Quixote; Alí and Conrad in Le Corsaire; Solor in La Bayadère; Prince Desire in Sleeping Beauty; Romeo in Romeo and Juliet; Colás in La Fille mal Gardée; Danilo and Camilo in The Merry Widow; Prince Siegfried in Swan Lake; Count Albrecht in Giselle, Aminta in Sylvia, 'Prince in Nutcracker'; Lensky in Eugene Onegin; Des Grieux in Manon; James in La Sylphide, Franz in Coppelia, among others. Neoclassical and Contemporary Ballets: Jerome Robbins' Francy Free and Other Dances; Twyla Tharp's Americans We, Push Comes to Shove, Sinatra Suite and Concerto No.1 for Piano and Orchestra; George Balanchine's Theme and Variations, Mozartiana Prodigal Son and Allegro Brillante; Frederick Ashton's Les Patineurs and The Dream, Eugene Loring's Billy the Kid; Stanton Welch's Clear and We Got it Good; Jiri Kylian's In the Middle is somewhat elevated, John Cranko's Eugene Onegin; Sinfonietta Petite Mort; Christopher Wheeldon's Henry VIII, Dance of the Hours, For 4, Mark Morris' Non Troppo and Drink to Me Only with Thine Eyes'; Clark Tippet's Bruch Violin Concerto, and William Forstye's In the middle somewhat elevated, among others

Ballets have been created on Corella by the choreographers Twyla Tharp, Christopher Wheeldon, Kevin McKenzie, John Neumeier, Mark Morris. Nacho Duato, Stanton Welch, Natalie Weir and Stanton Welch, James Kudelka, Lar Lubovitch and David Parsons.

In October, 1998, Ángel Corella danced four love songs sung by the famous mezzo-soprano Cecilia Bartoli during the Gala Opening Night of the ABT autumn season at New York's City Center. This experience was repeated in Spain on two occasions with the soprano Ainhoa Arteta; the first time in the Palau de la Música in Barcelona on 27 December 1999, and the second on 13 August 2000 in San Sebastian.

In May 2000, Corella received the Prixe Benois de la Danse Award for his work in Other Dances by Jerome Robbins, and on 4 November 2002, he was awarded "The National Dance Prize of Spain "as "an exceptional dancer and representative of a generation which enhances Spanish dance in the most outstanding international companies".

On October 2005, Angel Corella continued his association with the world of opera, performing the ballet Dance of the Hours in La Gioconda with Letizia Giuliani to choreography by Gheorghe Iancu at Theatre Liceo in Barcelona. The two performed in the same opera in September 2006, premering Christopher Wheeldon's choreography at the Metropolitan Opera House in New York. Both public audiences and critics gave enthusiastic receptions to each performance. During a Gala for the Victoria de los Angeles Foundation in January 2007, Angel Corella danced O mi Bambino Caro performing to a voice-over by Victoria de los Angeles.

Corella has danced for several leading international figures such as her Majesty Queen Sofía of Spain and the Infantas Elena and Cristina of Spain; Queen Elizabeth II and Princess Margaret of Great Britain, President George W. Bush and First Lady Laura Bush and President Bill Clinton and First Lady Hillary Rodham Clinton

Angel Corella, with his American Ballet Theatre colleague, Ethan Stiefel, is a co-creator of "Kings of the Dance", performing in 2006 and 2007 with Johan Kobborg, of England's Royal Ballet and Nikolay Tsiskaridze of the Bolshoi Ballet.

In 2001, Ángel Corella formed a Foundation to promote classical dance in Spain and to offer the opportunity for the finest professional training to all dancers, regardless of their economic or social condition. After six years of work one of the main projects, the Corella Ballet, came to birth and started its activity on April 2008 at the Royal Place of La Granja (Segovia-Spain).

In 2008 he was awarded with the Comunidad de Madrid Arts International Medal and with Ciudad de Salamanca's Culture Star.

In 2009 The Galileo Award Foundation Committee formed by Jack Lang, Irene Papas, Irina Strozzi, Marco Giorgetti and Alfonso de Virgiliis gave to Ángel Corella the Galileo 2000 Award for "his exceptional talent".