The programmes, which are running for the first time in three years, will see the apprentice and graduate engineers undertake two-year courses.
Delivered in two phases, the apprenticeship programme will cover academic and hand-skills training to City & Guilds Level III followed by time spent at an aviation and aerospace training facility.
For the final 14 months, apprentices will work alongside engineers across the airline’s Heathrow line and hangar maintenance facilities.
Training culminates with an Engineering Technician Apprenticeship certificate and the opportunity to apply for a permanent role.
The airline expects the scheme to commence on 3 October and the closing date for entries is 15 May.
Graduate engineers will work across departments including propulsion, airframe systems, avionics, cabin and structures along with receiving practical experience with the maintenance teams.
Neil Ambidge, Virgin Atlantic’s vice-president of engineering and maintenance, who started his career as a graduate for the airline, said: "We’re committed to the development of our world-class engineering team, and I’m delighted to be offering these positions to a new cohort of candidates as we invest in the talent of the future.
"Aircraft engineering and maintenance offers a fascinating career path, and our apprentice and graduate programmes provide a brilliant opportunity to work across one of the industry’s youngest, greenest fleets."