The new recruits, due to start in September, will join the shipbuilding and maintenance teams.
BAE Systems have announced plans to recruit a record 568 apprentices next year to build the next generation of nuclear submarines.
The Government-backed scheme will take on 181 more people than last year across its 16 sites.
Positions last 42 months, with an average salary of £14,000 and a guaranteed job at the end.
Nigel Whitehead, group managing director, said: "Apprentices are a vital part of our talent pool."