Naomi Campbell - who was hired by the designer in the early stages of her career - described him as a "gentleman of fashion", also sharing a photo of herself on his catwalk with the caption: 'You made this come true".
Fellow model Karlie Kloss said that the world had "lost one of the most extraordinary people that I have ever met".
"Thank you for helping me become the woman I am today and for always inspiring me to be better," she wrote on her Instagram page. "There simply is no one else like you."
Designer Marc Jacobs tweeted that the "fashion icon" would be missed.
Diane von Furstenberg added: "Oscar de la Renta was a wonderful designer, a true Renaissance man. His voice will continue to sing in our hearts."
Vogue editor Alexandra Shulman spoke of the designer's enduring talent and legacy.
"Of all the designers in the world, Oscar de la Renta was the most reliable at designing clothes that made you feel beautiful," Shulman said on Vogue.co.uk this morning.
"He stuck to his conviction about how women should look - elegant, joyful, feminine - no matter how fashion changed, but his designs never felt old or hackneyed. If you wore one of Oscar's dresses you felt you looked your best, which is one of the reasons that he was so often a first choice for ball gowns, weddings and public appearances throughout the world."
The fashion world pays tribute on social media
He is survived by his wife; son, Moises de la Renta; his three step-children, Beatrice Reed, Charlie Reed and Eliza Bolen; three sisters; and nine grandchildren.
- Independent
