The Competition and Markets Authority said the firm must sell an asphalt plant in the Aberdeen area and a ready-mix concrete plant in Peterhead area.
It will also face a price control for asphalt produced in the Inverness area.
The move follows fears of a lack of price competition in north east Scotland after Breedon bought 18 sites from Aggregate Industries in April 2013.
Simon Polito, Chair of the Inquiry Group and CMA Deputy Chair, said: “Both these products are vital for construction projects and road building, much of which is funded by the public purse.
“It is therefore important to ensure customer interests are protected, which we are doing through the plant sales and price control.
“The markets for these products are local so the loss of a competitor in even a relatively small area matters – particularly when the cost and proximity of the production site are the most important factors for customers and in a market where most prices are negotiated.”
Breedon said: “The Company will now work with the CMA to finalise the terms of these divestments and undertakings within 12 weeks.
“Breedon has every intention of reaching agreement with the CMA as quickly as possible, in order that it can expedite the sale of the assets concerned and proceed with the full integration of the former AI businesses.”