The show will be directed by actor and filmmaker Kenneth Branagh, reports theguardian.com.
"'Hamlet' presents almost limitless possibilities for interpretation. I can't wait to explore them, with this great cast, at RADA. Kenneth Branagh and I have long talked about working on the play together, and now felt like the right time, at the right place," Hiddleston said in a statement.
"To be guided through it by him as a director, an expert and a friend, is our great good fortune. The performing arts exist to bring people together, not to break or keep them apart," he added.
Funds raised from the production, which will have a three-week run at RADA's 160-seat Jerwood Vanbrugh Theatre, London, from Sep 1-23 this year, will support the RADA Attenborough Campaign, which is aiming to make money to regenerate the Academy's Chenies Street premises.