The pitch process was handled by Creativebrief.
PRWeek understands that Hope & Glory and Freuds were involved in the final pitch stage.
In March PRWeek reported that the legion was looking for a new PR agency.
The Academy is to develop a long-term PR strategy and create campaigns that ensure the organisation maintains its relevance among a younger audience. The Academy's team will be led by managing director Nicky Law.
Gary Ryan, director of marketing and comms at Royal British Legion, said: "The Academy stood out to us for its strategic approach and creative ideas. Although it is a relatively new agency, Mitch and Dan bring a wealth of experience and expertise to the table, and they will be working closely with our in-house team to deliver long-term PR strategy for the charity."
Mitchell Kaye, The Academy CEO and co-founder, added: "To help write the next chapter of the story for such an iconic organisation is a huge challenge for our agency and one we cannot wait to begin."