The contractor has an option to go on to construct the railway, bringing trains to the Borders for the first time since 1969.
Network Rail’s decision to appoint Bam Nuttall is the first sign of progress on the project since two of three bidders pulled out of the Scottish Government’s procurement process, causing it to collapse in September.
Bam was left as the sole bidder for the project after first Balfour Beatty and then Carillion pulled out because of concerns about the funding model.
The route, then due to be reopened in 2014 after a gap of 45 years, was to be built using a novel “non-profit distributing” approach, untried on the railways.
This led Transport Scotland to commit to funding the project, which will now be run by Network Rail.
Bam Nuttall’s team will draw up designs for the 35-mile railway route, including bridges, tunnels and stations. A total of seven new stations are planned.
David Simpson, route managing director for Network Rail Scotland, said: “This contract to deliver the design phase takes us and the Scottish Government one step closer to re-establishing a railway to the Scottish Borders.”
Transport Minister Keith Brown said: “This is an important project for the region and will help secure jobs and provide opportunities for communities along the route.”
Network Rail will also proceed with ground stabilisation works in the Midlothian section of the route where remediation of former mine works is required.