The scheme is open to people with five GCSE passes at C grade or above and who are expected to get the equivalent of two A levels by September this year.
The apprenticeships will start in October and involve 18 months working in at least one government comms team.
In return, GCS apprentices will be paid an annual salary of £20,188. An emphasis is being placed on attracting people from ethnic minority backgrounds, as part of a wider drive to improve diversity within the civil service.
"We welcome applications from people of all backgrounds, especially from groups that are underrepresented in government: Black, Asian and minority ethnic people and people from disadvantaged backgrounds," states the GCS.
"Our employees should reflect the people we’re communicating with and we welcome your application whatever your background. Bring your different views and experiences and help us make sure our campaigns are relevant and appealing to everyone," it adds.
Stereotypes are being tackled head-on by the GCS, in the careers section of its website, which says: "Imagine yourself as a government communications apprentice. What do you see? An office full of middle-aged, middle-class men in suits? A formal, intimidating environment?"
It adds: "There was a time when you might have been right. But government communications have changed. If you’re bright, enthusiastic and have ideas on how to get people talking about things that matter, we want you to join us."
The GCS is also using case studies as a comms tool to promote the apprenticeship scheme, now in its second year. Giorgio Di Tunno, one of last year’s apprentices, has been profiled. He began his apprenticeship after leaving sixth form, aged 18, and said: "I wake up motivated every day, knowing I’m doing something I enjoy whilst making a difference."
The government wants "digitally savvy" communicators with a passion for news and current affairs, according to the Cabinet Office.
The deadline for applying is the end of this week and successful applicants will gain experience of areas such as internal communications, digital and social media campaigns management and strategic engagement.
The new apprentices will study for a Level 3 Non Vocational Qualification in marketing but the Government is currently developing a PR and comms standard, which will replace the marketing framework currently in place.
The Cabinet Office said the apprentices would be paid the "equivalent of the UK Living Wage" and that the scheme provided a route for people from diverse backgrounds into the civil service.
A Cabinet Office spokesperson added: "The communications specific apprenticeship is designed to bring talented young people into GCS who would not have previously considered a career in government. We are committed to improving the future diversity and inclusivity of our profession by better representing the communities we serve."