His permanent appointment cannot be confirmed as yet due to a stand-off between Rupert Murdoch's News Corporation and the paper's independent publishing directors.
The Guardian reports that News International CEO Mike Darcey issued a statement on Friday that Witherow, who has been editor of The Sunday Times since 1994, will take over at the Times "effective immediately".
In an internal email, Martin Ivens, who has served as deputy editor on the Sunday Times since 1996, was promoted to acting editor of the paper.
However, neither appointment could be endorsed as permanent due to the independent directors being engaged in a row with News Corp.
The directors want a review of whether the papers should and will be merged, given what is currently described as their "very difficult financial position".
News Corp claim that they currently have no plans to merge the papers. Murdoch promised Margaret Thatcher's government upon taking over the publications in 1981 that they would remain distinct.
Witherow will replace James Harding, who edited the Times for five years. Harding resigned after it had been "made clear" that News International was seeking a new editor.