PR for the brand was previously handled in-house from offices in Brussels and Scandinavia.
The company wants to boost awareness of products Flymo is less associated with, such as hedge trimmers.
Golley Slater's brief will cover 19 countries. The account is headed up by Twickenham-based account director Catherine Greenwood. The agency beat Tonic Life Communications to scoop the brief, worth about £100,000.
Electrolux recently moved production of its flagship lawnmower, the Automower, from Scandinavia to its plant in North East England.
Electrolux launched the Automower, which is now sold widely across Europe, in 2004. The plant produces more than £1m-worth of lawnmowers a year.