More than 500,000 Australians have signed the petition to parliament since it launched three weeks ago.
News Corp Australia controls 70% of local newspaper circulation. Mr Murdoch has not commented on the petition.
The petition will likely be presented to parliament, but it is not obligated to act on it.
Mr Rudd, a Labor prime minister from 2007-2010 and again in 2013, has been a frequent critic of Mr Murdoch and his newspapers, which advocated against his re-election.
He praised the level of public response on Wednesday, saying he was “grateful and overwhelmed”.
“Half a million Australians have spoken. They’ve smashed the records to make their voice heard: Australia needs a #MurdochRoyalCommission to protect the lifeblood of our democracy,” he tweeted.
Like Mr Murdoch, News Corp has not responded to the public petition and have ignored it in their news coverage.
What is the criticism?
Among recent controversies, News Corp’s titles have been accused of minimising the role of climate change in reporting last summer’s bushfires, and publishing some misleading reports about the spread of coronavirus and the effect of lockdowns in Australia.
Employee attacks News Corp’s ‘irresponsible’ fires reporting
Murdoch tabloid defends ‘racist’ Serena cartoon
Murdoch’s son criticises Australia fires coverage
The company has defended its journalism against accusations of political bias, racism and climate change scepticism. Its newspapers are among the best-selling in Australia.
Mr Rudd’s petition calls for a royal commission – Australia’s highest form of public inquiry – into the “abuse of media monopoly in Australia in particular by the Murdoch media”.
Locally, Mr Murdoch owns 14 of 21 metropolitan daily and weekend newspapers, plus radio stations, TV channel Sky News Australia and top-read site news.com.au.
News Corp Australia also has the only metropolitan newspapers in Queensland, South Australia, Tasmania and the Northern Territory.
A kiosk displaying the front pages of The Daily Telegraph newspaper in Sydney
IMAGE COPYRIGHTGETTY IMAGES
image captionMurdoch controls a majority of Australia’s newspaper front pages
The petition also calls for scrutiny of Australia’s dwindling media diversity, alleging News Corp’s power has grown in recent years as other outlets have folded or been subsumed.
Murdoch buys and shuts 112 Australia community newspapers
Mr Rudd has described Mr Murdoch and his influence as a “cancer on our democracy”. In recent weeks, Murdoch papers have published unfavourable stories about Mr Rudd.
Another recent ex-Prime Minister, Malcolm Turnbull, has also consistently criticised Mr Murdoch’s power over Australia’s two major political parties.
He has signed the petition, and is among other high-profile figures, such as British actor Hugh Grant, who have expressed support for the probe.
What happens now?
Signing for the petition closed on 4 November with 501,766 signatures registered on the Australian parliament site. The petition was so popular in its first few days that it overwhelmed the parliament’s website.
The petition will likely be presented to parliament. However, unlike some nations, Australia’s government is not obligated to respond or act on it.
As the petition has not received the support of the ruling Liberal-National government or the Labor opposition, observes say this also makes it unlikely that such public groundswell will lead to the instigation of a royal commission inquiry.