The firms made the announcement following years of campaigning by unions after it was discovered that more than 3200 names, including 574 from Scotland, were kept on the list drawn up by an organisation called The Consulting Association (TCA).
A total of 44 firms were found to be using the blacklist. Workers involved claimed they were denied work often for raising legitimate concerns about health and safety on building sites.
Even though TCA was closed down in 2009 after a raid by the Information Commissioner's Office, unions said workers continued to be discriminated against if their names were included.
Now eight major firms say they are working together to develop a scheme to compensate construction workers whose names were on the database.
A statement said: "The companies - Balfour Beatty, Carillion, Costain, Kier, Laing O'Rourke, Sir Robert McAlpine, Skanska UK and Vinci PLC - all apologise for their involvement with TCA and the impact that its database may have had on any individual construction worker.
"The companies have joined together to establish the Construction Workers Compensation Scheme. The scheme is intended to make it as simple as possible for any worker with a legitimate claim to access compensation.
"The companies have invited workers' representatives to enter into a period of engagement to ensure that the proposed terms of the scheme are fair and effective. The group is also engaging with other interested parties."
Grahame Smith, general secretary of the Scottish Trades Union Congress (STUC), said the news was a vindication of the campaigns run by the unions on behalf of members and former members.
He said: "Clearly the compensation scheme proposed will need to meet the responsibilities owed to blacklisted workers both in terms of the scale of compensation offered and to cover the variety of circumstances and effects of each case.
"We welcome the apparent commitment to engage and negotiate the terms of the scheme with blacklisted workers and their union representatives. This will be key to achieving an agreeable outcome."
The announcement was welcomed by Jim Sheridan, MP for Paisley and Renfrewshire North and chairman of the Unite Parliamentary Group. However, he said it was long-overdue.
He said: "Blacklists denied people work simply because they wanted to work is a safe environment or were members of a trade union.
"While the apology and announced compensation scheme are positive steps, I think there is still more to be done before we can claim victory. Had the Office of the Information Commissioner not uncovered proof of the use of blacklisting I doubt these firms would be accepting responsibility or compensating workers for their criminal actions."
The Blacklist Support Group said it welcomed the proposals, but added: "So far there are no firm proposals, only a vague promise of compensation for any workers with a 'legitimate claim'.
"Forgive us if we do not crack open the champagne just yet. We do not for one second believe that these companies have suddenly seen the light. Most of the senior managers implicated in the blacklisting conspiracy are still in post.
"The only thing they regret is being caught."
Unite assistant general secretary Gail Cartmail said the priority should be to get blacklisted workers back into work and Justin Bowden of the GMB union said the next step for the firms was to "clean up and pay up."