The firm aims to move its primary listing to the US in the next 12 to 18 months, but it will keep a UK listing as an international company.
The company, which hires out construction equipment, has more than 25,000 employees.
Ashtead said annual profits would be lower than expected due to “local commercial construction market dynamics in the US”, which is set to affect rental sales growth.
Firms worth hundreds of billions of pounds have been quitting the London Stock Exchange for the US over the past few years, prompting concerns over how attractive the UK for investment.
These include Cambridge-based microchip giant ARM Holdings, which now sells its shares in New York, and Paddy Power’s owner Flutter.