Freeman, star of The Office, Sherlock and The Hobbit on screen, will "be in rehearsal by late May or early June of this year, and in performance by July", according to the Daily Mail.
Lloyd himself confirmed the news on Twitter last night.
Thanks for your tweets about Martin Freeman's Richard III @TrafTransformed. More details about booking etc will be available in the morning.— Jamie Lloyd (@lloydjamie) April 3, 2014
Richard III, which will run until September, is one of four new plays in the season, further details of which are expected to be announced in the coming days.
Martin Freeman's theatre credits include Clybourne Park, Kosher Harry (Royal Court), The Exonerated (Riverside Studios) and Blue Eyes and Heels (Soho Theatre).
On film, he has appeared in Hot Fuzz, Breaking and Entering, The Hitchhikers Guide to the Galaxy, Confetti and Love Actually.
Freeman's Sherlock co-star Benedict Cumberbatch is also soon to tackle the Bard on stage - his Hamlet will play the Barbican next year.
Lloyd's previous season at Trafalgar Studios - which ran under the banner 'Trafalgar Transformed' - included Macbeth starring James McAvoy, The Hothouse with Simon Russell Beale and The Pride featuring Hayley Atwell.