Founded in 2015 by chef Julien Royer in collaboration with the local Lo & Behold Group, Odette features a fusion of French cuisine with Asian influences, including of Singapore's.

[4][14] Singaporean artist Dawn Ng, who is married to Royer's business partner Wee Teng Wen, created a hanging installation in the main dining area called A Theory of Everything.

Inspired by Royer's focus on simplicity in the kitchen, Ng took printed photographs of ingredients, sticking them onto oak panels and folding them.

[13] While working at Jaan, regular customer Chong Siak Ching, the CEO of the National Gallery, asked if Royer would be interested in occupying an available space at the museum.

After meeting with a local business partner, he agreed after a couple of weeks to open his own restaurant there,[6] resigning from his position at Jaan in June 2015.

[13] In October, it was announced that Royer and managing partner Wee Teng Wen, of Lo & Behold Group, would be opening Odette in the National Gallery on November 2.

[13] During the COVID-19 pandemic, Odette made adaptations to their business, such as installing air and surface purification systems inside the restaurant, and implementing curbside pickup for take-out orders.

[5] The take-out service, Odette at Home, gives people the opportunity to order a multi-course meal from a curated list of menu items, without needing to visit the restaurant in-person.

"[21] The Straits Times' Wong Ah Yoke describes the atmosphere as "classy yet not ostentatious", and that the neutral color scheme is "contemporary, soothing and elegant".