The date was shared with The Associated Press by two diplomats from member countries of the UN's International Atomic Energy Agency.
They demanded anonymity because they were not authorised to reveal it before a formal IAEA announcement.
The November 24 deal commits Tehran to curb its nuclear programs in exchange for initial sanctions relief over six months as the two sides work toward a permanent agreement.
The accord designates the IAEA to oversee Iranian compliance with terms of the deal. The 35-nation IAEA board is expected to approve that role at the January 24 meeting.