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.
This cost will be recouped at least partly through tolls. While the price of tolls is not known, the longer M6 Toll currently charges £5.50 for a car and £11 for a lorry on weekdays.
More top news
There has been a sharp and worrying rise in the number of youngsters contacting ChildLine about suicide, the children's charity warned.
A travel firm will try to promote North Korea trips to UK holidaymakers - despite the country's current ban on visitors over Ebola fears.
One person is still unaccounted for following a large blaze at a fireworks factory in Stafford.