Transport Scotland announced its intention to award the contract to Interserve, which involves the construction of a one kilometre section of carriageway, situated between Beith and Dalry, including new junctions.
The £9 million project will also remove a series of sub-standard bends on the existing road, improve traffic flow and introduce safety benefits.
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Michael Matheson, Cabinet Secretary for Transport, Infrastructure and Connectivity, said: "The Scottish Government is committed to improving Scotland's transport infrastructure and today's announcement further cements our investment in the A737.
"These improvements - along with the current work to construct a Bypass at Dalry, which is less than a mile from the Den, and currently a year into construction - will deliver benefits for the North Ayrshire communities as well as long-distance road users upon completion."
The one kilometre of carriageway will be constructed off-line.
Subject to a mandatory standstill period, construction is expected to get underway in the coming months with completion expected in Spring 2020.
(CM/MH)
