The global pitch was won out of the New York office. The network is working on a creative route that can be translated for a range of markets around the world.
The distiller, which did not previously retain an agency in the UK, kicked off the pitch process last year, following a decision by Bacardi-Martini to turn Dewar's into a global brand.
The company has previously run TV ads in South America, Thailand and Greece featuring Sean Connery superimposed on to a clip of a James Bond film.
The ad shows the actor speaking to the younger version of himself. The tagline says: "Some things age, others mature."
Dewar's has three whisky brands: White Label, Dewar's Signature and Dewar's 12. The ad brief will be based on pushing the brands into global markets.
Saatchis joins Fallon and Campbell Doyle Dye on the Bacardi roster.
The distiller was founded as John Dewar & Son in the 19th century. The father-and-son team originally started as a grocery business that blended teas but quickly moved into distilling whisky.
United Distillers & Vintners acquired the company in the 70s, then Bacardi-Martini took it over in 1998.
At the time of going to press, Saatchi & Saatchi was unable to comment.