The Barcelona-born costume designer dressed Eddie Redmayne in his riveting portrayal of Lili Elbe, the first person to undergo early form of gender reassignment surgery in 1930.
The designer has worked with The Danish Girl director Tom Hooper and Redmayne in the past, when he earned an Oscar nomination in 2013 for his work on the film Les Miserables.
He has won two Goya awards for Best Costume Design; With Biancanieves in 2013 and Las Brujas de Zugarramurdi in 2014.
In The Danish Girl Delgado was faced with the challenges of designing for a character that was undergoing a transition from a man to a woman during a period defined by a very particular style.
"Eddie was very worried because he wanted to create a female figure with a waist, and that had two problems: first, that a man's body doesn't normally have a waist," he said in a recent interview with Harpers Bazaar.
"And second, we are working in the '20s where the waist disappeared completely in the shape. But from very early on we just discovered and decided that Lili herself was using what she saw were advantages of the fashion sense of the period. We tried to recreate the fashion that was appropriate for her.
The designer is also recognized for his work on the 2010 film Biutiful starring Javier Bardem and the 2011 film The Skin I Live In, directed by Pedro Almodóvar and starring Antonio Banderas.
He is the only Spaniard on the Oscar nominations list for 2016.