Farmar played in Israel during the NBA lockout last summer and has indicated he may return to Europe.
The Hawks also received guards Anthony Morrow and DeShawn Stevenson, and forwards Jordan Williams and Johan Petro, as well as first- and second-round picks, in the deal which became official on July 11.
The Hawks are saving salary cap space by removing Farmar from their roster.
The 6-foot-2 Farmar averaged a career-high 10.4 points in 39 games, including five starts, with the Nets last season. Farmer was drafted out of UCLA by the Los Angeles Lakers with the No. 26 overall pick in the 2006 draft.