He said it was the right time to step down from the position.
Ponting said he wanted to play on as a batsman for Australia because he still had plenty to offer a young side.
"I want to continue to lead by example both on and off the field," he said.
"... I'm around for advice if needed."
"I'm really excited about...the next chapter of my life as a player," he said.
He said he will give the next Australian captain his full support.
Ponting endorsed Michael Clarke as his successor, saying the New South Welshman had done the job well for Australia at Twenty20 level and in one day matches when Ponting was absent.
He said Australia's exit in the quarter-finals of the World Cup last week prompted his decision to stand aside as skipper.
"The fact that we went out of the World Cup when we did was the main reason," said Ponting, while denying he had been tapped on the shoulder by anyone at Cricket Australia (CA).
Following a recent lean stretch with the bat, the Tasmanian ended his run drought in the quarter-final with a stellar century as his side lost to India.
Australia heads to Bangladesh early next month for a short tour including three one-day internationals.
Ponting wants to be a part of the touring squad.
Ponting has spent the vast majority of his career batting at No.3 and believes it remains his best position in the order.
"I still believe it is but we'll wait and see what the next captain has got to say about that," he said.
Ponting has lost three of four Ashes series as skipper - including two in England - and said he would love to have one more crack at winning the famous urn back in 2013.
The CA board will meet later on Tuesday to consider who will replace Ponting as skipper.
Their recommendation will be taken to the national selectors, with an announcement scheduled for Wednesday.
CA chairman Jack Clarke paid tribute to Ponting's leadership.
"Ricky Ponting has been an outstanding batsman, one of the best to wear the baggy green," Clarke said in a statement.
"His leadership as captain has been outstanding and I sometimes think his brilliance with the bat has overshadowed his fine work as captain.
"Those close to the team know his true worth in guiding his players and setting a personal example of commensurate professionalism, particularly in recent years following the retirement of so many greats of the game."
Ponting captained Australia in 77 Test matches for 48 wins - the most of any Test skipper - 16 losses and 13 draws.
His 227 one-day matches in charge returned 163 wins, 50 losses and two World Cups.
