Mr Graham enters the role following the resignation of Christine Holgate, who stood down following public and political outcry of executive spending.
During Senate Estimates hearings it was revealed Ms Holgate purchased four Cartier watches worth approximately $20,000 to reward executives for delivering on a deal that would net the organisation millions.
In a public statement today Australia Post Chairman Lucio Di Bartolomeo said Mr Graham enters the role with 40 years of experience in complex logistical businesses.

"On behalf of the board I am so pleased to announce Paul as the next CEO of Australia Post – an outstanding candidate with strong logistics, digital and retail experience both here and overseas, including as a senior executive at Deutsche Post DHL," Mr Di Bartolomeo said.
"Paul has a demonstrated track record of delivering results in large, complex organisations and is a proven leader managing large teams.
"The Board was impressed by Paul's 40 years' of deep industry experience working in supply chain in Australia, Europe and Asia.
"We are also confident Paul's community and customer philosophy is a perfect fit for Australia Post."
Mr Graham said he was proud to be appointed CEO and pledged to make customers "at the centre of everything we do".
"Australia Post has proven itself to be one of the most resilient and successful postal businesses anywhere in the world. I feel fortunate to be joining at a time when we can truly capitalise on the extraordinary growth in eCommerce experienced in the past year and continue developing our retail and digital offerings while keeping letter deliveries strong," Mr Graham said.
"I am most looking forward to meeting the team across the country – the posties, Post Office workers, mail processors and delivery drivers that kept our country operating during COVID-19.
"I am also looking forward to getting out into regional Australia where Australia Post has an enormous presence, as well as meeting with the thousands of Post Office licensee partners who play a critical role every day serving the country."
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