The announcement was made as part of a five-year plan, which includes improved rail services and promotion of greener transport, such as cycling and car-sharing schemes.
Mr Jones, who also holds the transport portfolio, had announced plans for the 14-mile (22.5km) M4 relief road in September 2007, saying the scheme, proposed to run from Magor to Castleton, could open in 2013.
It came after two crashes in previous months had caused gridlock to the south Wales corridor, prompting business leaders to say the economy of the area had been affected by the traffic congestion.
In his statement on Wednesday, Mr Jones said putting tolls on the "unaffordable" proposed new road would have reduced its economic effectiveness.
He said putting tolls on the existing motorway as well as the relief road would be "unacceptable to business and the travelling public" given there were already tolls at the two Severn crossings.
He said the assembly government would instead spend between £64m and £110m improving the existing M4 network
Measures would include improvements around Tredegar Park junction, the Brynglas tunnels and the Coldra roundabout, bringing into public use a seven-mile dual carriageway through the Corus site in Newport, and improving the southern distributor road through Newport.
Mr Jones said he was aware of the arguments for and against the M4 relief road.
He said: "I understand and share the concerns both about capacity, safety and resilience of the M4 as well as the environmental impact of the proposed relief road."
"My message to businesses and the wider community in this part of Wales is that this government is committed to reducing congestion, restoring capacity, reliability and improving safety on this important East/West corridor."
Neil Crumpton, of Friends of the Earth Cymru, said axing the motorway plan provided "a huge opportunity for the assembly government to resolve the M4's increasing safety and maintenance problems by investing in much more cost-effective and less damaging measures along the M4 and other local routes".
He said: "Ieuan Wyn Jones is to be congratulated for taking this bold decision in the face of a growing climate crisis."
On the airport access road, Mr Jones said "only a fraction" of the benefits a proposed airport link road would bring the area were associated with the airport.
As an alternative, he said the assembly government would investigate a half-hourly bus express bus service from Cardiff city centre to the airport, more frequent train services and improved safety on the A4266 (Five Mile Road).
Cardiff Airport said it welcomed the decision to "end the uncertainty" and also the "more pragmatic and sensible approach" to enhance public transport options between the airport and the city.
"We would encourage immediate discussions in this regard as the relevant public transport standards need to be addressed."
But Vale of Glamorgan MP John Smith said the decision not to go ahead with the airport relief road was "economic lunacy" and a "reckless decision for the Welsh economy".
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