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.
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The morning will be mostly dry with some bright or sunny spells. However, cloud will thicken from the west during the afternoon.
Kenyans Eliud Kipchoge and Vivian Cheruiyot won the men's and women's races respectively, in a scorching hot London Marathon.
Most areas will have a dry night with some clear spells.