Alastair Campbell was the spokesman for former prime minister Tony BlairCopyright: Fiona Hanson/PA
Sir Harold was also involved in an attempted management buyout of the Sunday Times, but was defeated by News Corporation chairman Rupert Murdoch's takeover bid in 1981.
Rupert Murdoch has already given evidence to the inquiry about a meeting he had with former prime minister Margaret Thatcher three weeks before his successful bid for the Times and Sunday Times, which he insisted was "quite appropriate" and "perfectly right".
Sir Harold had alleged on BBC Radio 4's Today programme in March, the month prior to Murdoch's Leveson appearance, that Thatcher and Murdoch appeared to have "cooked a deal".
Other witnesses confirmed for the inquiry next week include MP Jack Straw and Sky News political correspondent Adam Boulton.
The inquiry is now in module three, which is looking into the relationship between press and politicians. Evidence will be heard from Monday to Thursday next week.