Each of the three design contracts is estimated to be worth between £40m and £60m.
Consulting engineer Jacobs has been appointed to design the upgrade for the 32-mile stretch between the Pass of Birnam and Glen Garry.
As previously reported, a joint venture of CH2MHill and Fairhurst was appointed in April for the 27-mile stretch between Glengarry and Dalraddy.
Subject to the mandatory standstill period Jacobs will start work on the section of the route nearest to Perth next month.
Transport minister Keith Brown said: “This second major contract is another step forward for this mammoth project, and underlines our determination to bring forward benefits to road users as soon as we can.
The third and final design contract to dual the A9 between Dalraddy and Inverness is expected to be awarded by the end of this year.