Work on the project is expected to begin in the "coming weeks".
The award is to a consortium of Sacyr, Wills Bros and Somague.
Sinn Féin's Elisha McCallion MP welcomed the announcement: "The £220million project involves the creation of almost 26 kilometres of high-standard dual-carriageway between Dungiven and Drumahoe.
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"Derry city and the north west region has been crying out for meaningful investment of this kind.
"This scheme will transform life for citizens and commuters in the area, and I look forward to its eventual completion."
SDLP Foyle MLA Mark H Durkan said: "This is great news and people in Derry are delighted to hear and see that these long, long overdue and very badly needed road improvements are progressing.
"Improved connectivity is vitally important not only for attracting investors and tourists to our beautiful city but also for improving road safety and reducing travel time for the many who have to travel towards Belfast for work or study.
"We acknowledge the work of all involved to get this far but much more is still needed to address our infrastructural deficit."
(CD/MH)
