In a decision letter published yesterday, Drakeford contradicted the inspector, who had recommended the approval of the scheme after concluding that its benefits would outweigh any negative environmental impacts.
However, the first minister said the benefits were unlikely to materialise due to a previous decision by the Welsh Government not to provide funding for the scheme.
Drakeford’s letter said: "If I were to make the schemes and orders in circumstances where the project would not be implemented in the foreseeable future, I consider that it would result in those persons and bodies affected by the schemes and orders being subjected to continuing uncertainty for a considerable period of time."
The proposed congestion-relieving scheme would have provided a 23km dual carriageway motorway from Magor to Castleton, passing south of Newport.
It would have included a new bridge, and alterations to Newport Docks.
The Welsh Government has estimated the cost of the road at £1.6 billion, and in April decided not to financially support the project.
However, in his letter, Drakeford said that even if that decision had not been made, he would still have refused permission for the road.
He said he attached greater weight than the inspector to the adverse impacts of the project on the environment.
He said: "In particular, I attach very significant weight to the fact that the project would have a substantial adverse impact on the Gwent Levels sites of special scientific interest and their green network and wildlife, and on other species, and a permanent adverse impact on the historic landscape of the Gwent Levels."
Reacting to the decision, Justin Millett, lead director in consultancy JLL's Cardiff office, said the relief road could have shored up demand for new warehousing and distribution space in the area.
He said: "This decision risks a two-tier land market in South Wales with land and property on the east side of the Brynglas tunnels outvaluing areas to the west."
In April, plans were approved for a new 2.6km bypass around Middlewich in Cheshire, in line with a recommendation from planners who advised that the scheme would help enable the delivery of housing and employment sites in the area.
Also in April, Cornwall Council gave the go-ahead for a 6.2km link road between St Austell and the A30, after officers said the scheme would support new housing development and regeneration in the county as well as deliver "significant environmental benefits".