The polls come after the 77-year-old president Michael Sata passed away in London in October from an undisclosed ailment.
Guy Scott said the election will be held in accordance with the Zambian constitution, within 90 days of Sata’s death.
“The presidential by-election shall be held on Tuesday, 20 January 2015,” said Scott.
Both the ruling Patriotic Front and the opposition Movement for Multi-Party Democracy (MMD) enter the campaign split by leadership battles.
The battle to take control of Sata’s party has spilled into the courts.
Meanwhile former president Rupiah Banda has said he will run for the MMD party.
The party president, Nevers Mumba, who contested that declaration and had been tipped as the likely party candidate, was suspended on Tuesday.
“We have with immediate effect charged and suspended party president Nevers Mumba,” said national secretary Muhabi Lungu.
Although born in Zambia, Guy Scott’s parents are not Zambian, so he is barred from running under the current constitution.