Addressing the media more than 12 hours after the party room ballot, Mr Abbott said that leadership challenges were never easy.
"This is a tough day, but when you join the game, you accept the rules."
He said his government had achieved a lot, despite “white anting”.
“My pledge today is to make this change as easy as I can,” he said.
“There will be no wrecking, no undermining, and no sniping. I've never leaked or backgrounded against anyone. And I certainly won't start now. Our country deserves better than that.
“I want our government and our country to succeed.”
Mr Abbott thanked his family, staff and Chief of Staff Peta Credlin, who he said had “been unfairly maligned by people who should've known better”.
But Mr Abbott did have a shot at the febrile media culture that rewarded treachery.
And he had some advice for the media as well.
"Refuse to print self-serving claims that the person making them won't put his or her name to," he said.
"Refuse to connive at dishonour by acting as the assassin's knife.
Mr Abbott outlined the good record of his government, citing the creation of 300,000 jobs, abolition of Labor's carbon and mining taxes, the signing of free-trade agreements with Japan, South Korea and China and the biggest infrastructure program in Australia's history.
WATCH: How have Australians reacted to Tony Abbott's departure?
"We've responded to the threats of terror and we've deployed to the other side of the world to bring our loved ones home."
"The boats have stopped and with the boats stopped, we've been better able to display our compassion to refugees."
“I’m proud of what we've achieved over the past two years,” he said.
"Of course, there's much that I had still wanted to do. Constitutional recognition of Indigenous people. Getting the kids to school, the adults to work and communities safe. I was the first Prime Minister to spend a week a year in remote Indigenous Australia. And I hope I'm not the last.”
Australia also had a role to play in the struggles of the wider world including the Middle East cauldron and in the South China Sea and elsewhere.
"I fear that none of this will be helped if the leadership instability that's plagued other countries continues to taint us."
He said his government “wasn’t perfect”, but gave it his all.
"We have been a government of men and women, not a government of gods walking upon the earth."
“I have rendered all and I am proud of my service,” he said in closing.
“My love for this country is as strong as ever, and may God bless this great Commonwealth.”
Mr Abbott did not take any questions.
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Transcript: Tony Abbott's final address as Prime Minister
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