It comes in the wake of Prime Minister Malcolm Turnbull's decision not to nominate him to run for the UN's top job of secretary-general.
Mr Rudd argued the UN writes too many reports and has rigid institutional silos.
He also offered prescriptions, including that the UN prioritise field operations over head office and better include women.
"Given the recent decision of the current Australian Prime Minister to decline my nomination, it seems I will not be a candidate myself for the position of UN secretary-general," he writes.
"But I offer these reflections, and more substantively the report I will soon release, to the next secretary-general, her or his staff, the UN secretariat, and most importantly the UN member states, for their consideration."
Rudd's failed bid does not affect Australia's reputation: professor
Last week Mr Rudd told The Australian newspaper Mr Turnbull's decision not to nominate him for the role of UN secretary general would damage the PM's international standing.
Alan Tidwell, the Director of the Centre for Australian, New Zealand and Pacific Studies at Washington's Georgetown University. disagrees.
"I think the impact of Prime Minister Turnbull's decision not to nominate Kevin Rudd or support the nomination of Kevin Rudd for the secretary-general is really a non-issue at the end of the day," he said.
"It affects Kevin Rudd, absolutely, but does it affect Australia's reputation? Not at all."
Commentators have suggested the United States Democratic Party's presidential nominee Hillary Clinton, who once described Mr Rudd as a friend, may raise the issue with Mr Turnbull.
But Professor Tidwell also rejects that theory, and said he cannot see a future Clinton presidency "making comment one way or the other" on Mr Rudd's nomination.
"I's a decision made by the international community," Professor Tidwell said.
"It's a collective vote.
"I can't see the Clinton administration, or any president for that matter, using political capital in that way."
'Time to back' former NZ PM Clark
Mr Rudd's critics argue his behaviour since Mr Turnbull's decision — releasing private letters and giving a tell-all interview insisting Mr Turnbull had previously backed his push for the job — has vindicated the Prime Minister.
Mr Turnbull has since confirmed he did not think Mr Rudd had the temperament or interpersonal skills needed to do the job.
But Professor Tidwell is not convinced tales of Mr Rudd's short temper have gained much traction in the United States.
"Kevin Rudd is not the only international leader who has a reputation for maybe a brittle ego, if you will, or maybe just a quick temper," he said.
"To say that that's a unique quality of Kevin Rudd I think is stretching the truth a little bit."
Professor Tidwell says the Australian Government should now get behind former New Zealand Prime Minister Helen Clark's bid for the position.