The 35-year-old Jayawardene said on the eve of the first Test against Australia that he thought next year would be a good year to make the transition to a younger leader as there were few high-profile series scheduled.
Jayawardene, who led Sri Lanka to the 50-overs World Cup final in 2007, agreed to take over the captaincy for a second spell in place of opener Tillakaratne Dilshan earlier this year.
"I don't want to continue to captain after this tour so this will be my last. I hope I don't get any more SOS calls from them," Jayawardene said in Hobart.
"It's been great, I've enjoyed the last year and what I've achieved but we need to move on to a younger leader. It's best that we get a new player in while the senior guys are still around so we can help him out in building a team."
Jayawardene said his choice to succeed him as skipper would be 25-year-old Mathews, who has matured into a world class all-rounder over the last couple of years.
"Angelo is the one everyone has earmarked, and I think he is good enough," Jayawardene added.
"Maybe the first few years will be tough for him but they'll grow into the job. If Angelo gets the opportunity, I think it will be easier for him if he has (the senior players) around him and we can build him through those tough periods."
- Sports & Recreation
- Tillakaratne Dilshan