Opertators Virgin said it had undertaken the biggest recruitment drive on the route since the days of British Rail in the 1980s.
There were almost 200 applications for each post, which come with a £57,000 salary when drivers become fully qualified.
They will ensure the smooth running of the operator’s new Azuma fleet, which will run between Scotland and London from 2018.
Virgin said a “significant” number would be based in Scotland, with Edinburgh one of five recruiting centres.
“We have received a huge amount of interest in this fantastic opportunity at Virgin Trains on its east coast route,” said a company spokesman.
“We are working hard to process and update all of the applications we received.
“Those who have been successful in getting through the first stages of the process will be invited to attend a selection day which will include a variety of assessments and exercises that will bring the best talent into our business.”
Over the course of a year trainees will take part in a mix of classroom-based and ‘on the job’ learning at different locations on the east coast route. Modules range from track safety, understanding operational route risks and emergency situations to getting to know the traction they will be driving.