The food company is also reviewing its media buying, currently held by Starcom, and has put together a shortlist of agencies.
EGS, launched by three former Starcom directors in March, will begin working for New Covent Garden in July.
Jez Groom, one of the new agency's founders, previously headed the New Covent Garden business at Starcom.
Nigel Parrott, New Covent Garden's marketing director, said: "EGS's business focus is about maximising the commercial return from creative media thinking and I'm looking forward to working with it to continue the successful growth of the New Covent Garden Soups brand."
New Covent Garden's most recent advertising has promoted its soup and new risotto and porridge lines with work from the creative agency Hooper Galton.