Ponting, 36, who led Australia in more than 300 Test and one-day matches, insisted there was no "tap on the shoulder" to step down and said he remained available for selection. He endorsed deputy Michael Clarke as his successor.
"I have thought long and hard about what Australian cricket needs. Now is the right time for the next captain to assume the responsibility for both the Test and one-day teams," he told a press conference.
Ponting is Australia's most successful Test captain and their leading Test run-scorer, and lies second only to India's Sachin Tendulkar on the all-time list of Test centurions.
But his record, straddling a transition period after the retirement of a host of greats, is tainted with three Ashes series defeats to England, along with occasional flashes of petulance.
Ponting said last week's World Cup quarter-final loss to India -- ending their 12-year reign as champions -- prompted his move, which also comes just three months after the latest Ashes loss brought strident calls for change.
"The fact that we went out of the World Cup when we did was the main reason," he said, while denying he had been forced out by Cricket Australia. "I will go on the record and say that I have had no tap on the shoulder from anybody, this has been a decision that has been wholly and solely made by me."
Ponting added that he was excited by the prospect of being unburdened by the captaincy and rediscovering his world-beating batting form.
His fighting 104 in Thursday's quarter-final was Ponting's first hundred in 39 international innings across all formats.
"Today is a new start for me and I am very excited about the future," he said.
"I will give my complete support to our new captain and continue to do my best to set the best possible example for my team-mates and emerging cricketers alike.
"I proved to myself the other day that I still have what it takes to play a good international innings and that was something that was really important to me."
Ponting endorsed his deputy Clarke as the next captain, starting with the three one-day match tour to Bangladesh in April.
"Absolutely. I think that is the way it will go, for the sheer fact that he (Clarke) has done a terrific job in almost every game he has had the chance to captain for Australia," he said.
"I think he's growing into the leadership role and I would totally endorse Michael Clarke as the next captain."
Ponting has been under growing pressure since earning the dubious distinction of becoming the only Australian skipper to fail to win the Ashes three times, and said he was proud of how he responded. "It's something I've had to deal with over the last six to eight months. There's been a lot of those questions out there about me, about my leadership, and even my batting at different times," he said.
"The thing that I am really proud about is how I have handled it and how I responded with the bat in the last game, under probably the most pressure that the team and I have been under for a long time, was really satisfying."
He did not say when he might retire altogether.
"I have not put a finish date or time on when my international career will be over. I haven't written off playing in the 2013 Ashes and to have another crack at winning another Ashes series in England," he said.
Ponting stands as one of the modern-day cricketing greats, amassing 12,363 runs in 152 Tests at 53.52, and 13,288 runs in 359 one-day internationals.
He has won more Tests as captain with 48 than any other Australian and has the astonishing success rate of almost 72 percent as the country's one-day leader, winning 164 of his 228 games.
"Ricky Ponting has been an outstanding batsman, one of the best to wear the baggy green," Cricket Australia chairman Jack Clarke said.
Cricket Australia meet later Tuesday to discuss who will succeed Ponting, with Clarke the overwhelming favourite.
