The Competition and Markets Authority (CMA) previously warned its deal could result in a substantial lessening of competition, leading to higher prices and lower quality building materials for UK construction projects.
Investigators said they were concerned about the supply of ready-mixed concrete, non-specialist aggregates or asphalt in 15 local markets across the UK.
Breedon, which has operations across Shropshire and the West Midlands, now plans to offload several ready-mixed concrete plants and an asphalt plant in England, two quarries and a cement terminal in Scotland to meet concerns.
This week the CMA said it believed that the undertakings might be acceptable.
Breedon said: "Breedon welcomes the announcement from the Competition and Markets Authority that it has reasonable grounds for believing that the undertakings offered by Breedon in connection with its completed acquisition of certain assets and operations from Cemex, or a modified version of them, might be acceptable.
"These undertakings will require the divestment of a small number of ready-mixed concrete plants and an asphalt plant in England, and two quarries and a cement terminal in Scotland.
"The company fully expects to be able to finalise the required undertakings to the CMA's satisfaction and complete the required divestments in the near future, paving the way for the integration of the remaining former Cemex assets into the group later this year."