It will become the second toll road in Britain - following the M6 in Staffordshire - and will run between junctions 23 and 29 of the M4 to relieve congestion on the outskirts of Newport.
The newspaper reports that the Chancellor will agree to guarantee loans for the building of the M4 relief road, but the devolved Welsh government will meet the cost - expected to be around £830 million.
More top news
The strong winds will ease overnight, but heavy rain is likely in places. At least it will feel mild!
Road closures, fallen trees and flooding hit all parts of Wales.
Two police officers who stole £10,000 during a raid have been jailed. South Wales Police say they "betrayed" public trust.