Jayawardene began his second stint as skipper in January after the departure of Tillakaratne Dilshan, and he will depart after the second Twenty20 at the MCG on January 28.
"I took over the captaincy for 12 months and that ends after this series, so I don't want to continue to captain Sri Lanka after this tour. This will be my last," Jayawardene said in a press conference ahead of the first Test in Hobart, reported on cricinfo.com.
"I was going to wait until the end of the series but I thought I might as well do it now, having had a chat to the selectors."
Jayawardene was previously Sri Lanka captain for four years to 2009, but took on the task again after Dilshan struggled.
His second reign has proved largely successful, most notably with the 1-0 Test series victory over then top-ranked England.
However, he has no interest in a third stint in the future.
"I hope I don't get any more SOS calls from them later on," he added. "This year has been brilliant. I've enjoyed and what I've achieved."
Jayawardene is now expected to help vice-captain Angelo Mathews prepare to make the step up.