News Corporation lobbyist Frederic Michel will also appear at the inquiry into press ethics and standards, it has been announced. They will both give evidence on Thursday, May 24.
Smith resigned last month after the Leveson Inquiry published a series of emails between him and Michel in relation to News Corp's bid to take full control of Sky.
The messages appeared to suggest that Smith kept News Corp in close contact during the bid process, and even hinted that the culture secretary was supportive of News Corp's aims in the Sky takeover.
Jeremy Hunt had asked for his scheduled appearance before Leveson to be brought forward so he could clear up controversy over his "quasi-judicial" handling of the Sky bid review. However, this request was turned down by Lord Justice Leveson.
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Also appearing at the inquiry next week will be former Labour cabinet minister Lord Mandelson, Lord Reid, Tessa Jowell and Alan Johnson.
Labour MP Tom Watson, a member of the culture select committee and a persistent critic of Rupert Murdoch's News Corp, is to give evidence at the inquiry next Tuesday (May 22).