The prosecution follows an HSE investigation into an incident in April where a motorway crash barrier being installed on the bridge plunged 25 m onto a grass verge alongside the A4 motorway below.
Last month, in a separate incident, four steel workers fell to their deaths from the bridge after the gantry they were working on plummeted to the ground, killing them instantly.
Three of the men were employed by Kvaerner Cleveland Bridge. The fourth was employed by Scottish steel firm Motherwell Bridge.
Costain and Kvaerner Cleveland Bridge were unavailable for comment.
The charges allege that both firms failed to ensure that members of the public were not exposed to danger from the work being carried out on the bridge.
The case will be heard before Bristol Magistrates鈥� Court in December and could be committed to the crown court.
The HSE investigation into the four deaths is continuing.
