Tony winner Mike Nichols will direct the production, which will reportedly open in March at the Barrymore Theatre.
Scott Rudin will produce the revival.
The New York Times confirmed the casting Aug. 12. Garfield, whose screen credits include "The Social Network" and "Never Let Me Go," won the Milton Shulman Award for Outstanding Newcomer at the 2006 Evening Standard Theatre Awards.
Hoffman last appeared on Broadway as James Tyrone, Jr. in Eugene O'Neill's Long Day's Journey Into Night. He garnered a Tony Award nomination for his work. He has also appeared in revivals of True West and Miss Julie. He earned an Oscar for "Capote," and nominations for "Charlie Wilson's War" and "Doubt."
Nichols' last Broadway outing was the short-lived revival of The Country Girl. He has received nine Tony Awards for works including Spamalot, The Odd Couple and The Real Thing. He earned an Academy Award for "The Graduate."