The first 55 km (34 miles) of the development will extend from the proposed Junction 8, located south of Strabane, to Junction 15 near Ballygawley, incorporating the westward expansion of the existing A4 dual carriageway.
Speaking after receiving Executive approval for the project to proceed, Minister O'Dowd said: "I am pleased to be able to outline the next steps for this crucial project.
"I can confirm that, following careful consideration of Planning Appeals Commission reports and the environmental impacts of the scheme, I have decided to start work with the first phase of the scheme, which will be between Strabane and Ballygawley.
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"This is in line with the PAC recommendation that this section should proceed in the wider public interest. This would be the first phase of construction work, covering over half of the total project, 55km or 34 miles out of 85km or 53 miles, with my intention to make a formal decision on the remaining sections at the earliest opportunity."
Sinn Féin MP Órfhlaith Begley has hailed approval by the executive to move ahead with building the A5.
The West Tyrone MP said: "This is a hugely positive day for people across the island as the executive has agreed to infrastructure minister John O'Dowd's proposal to move ahead with building the A5.
"My first thoughts are with each and every family who have tragically lost a loved one on this stretch of road. Today is for them and also in memory of those who have lost their lives.
"Transforming this road will save lives, create jobs and significantly cut journey times between the north-west and Dublin.
"Sinn Féin have made promoting regional balance a priority since our ministers took up office, and this is another step towards creating a fairer, more balanced economy.
"I will continue to work with the executive and the other parties to ensure this game-changing project is delivered in full."
