The work, originally due to start next month, is now planned to begin in September subject to a procurement process.
£16.2m has been allocated to Translink for the railway upgrade.
Last year, Translink said an hourly service on the route was a "priority".
The second stage of the upgrade involves major re-signalling between Derry and Coleraine and the introduction of a passing loop.
Work on a second major upgrade to the Londonderry-to-Coleraine railway line has been delayed by four months.