It is the first campaign Lucky Generals has created for the brand, since being appointed to the Pernod Ricard roster in October. It is also the first work the agency has done that will run outside the UK.
The four-minute ad, "the White Russian", will launch online and in US cinemas.
It will be supported by a behind-the-scenes series, instructional cocktail mixing films, consumer experiences and a retro movie poster campaign promoting Kahlúa’s classic cocktails.
The cinematic western styled film features The Big Lebowski star narrating an intriguing story about the unexpected encounter of two men from different worlds in the 1970s.
The ad was directed by the award-winning director Ivan Zacharias through Stink.
Bridges said: "As a short film entirely inspired by a simple classic cocktail, this story is creative, enigmatic and beautifully shot.
"The White Russian is one of the most popular classic cocktails and it's seeing a massive revival right now, so to work with Kahlúa on this project is great timing."