The 35-year-old Jayawardene confirmed 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 told reporters 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."
Meanwhile Jayawardene admits Sri Lanka do not expect Lasith Malinga to return to the Test side for the series against Australia, despite his six-wicket showing this week.
Malinga, who retired from test cricket earlier this year, gave a reminder of what a devastating bowler he can be by taking six for just seven runs in the Big Bash League yesterday.
Jayawardene today named a largely unheralded trio of seamers in his team for the first test and said it was unrealistic to ask the 29-year-old to return to the test arena.
"I think Lasith has made up his mind," he said. "With the injuries he has had over the last couple of years, I think it's unfair to ask him to come and play test cricket.
"He's in our one-day team and Twenty20 team and he's contributing a lot. Do we risk all that? Test cricket is about bowling 20-25 overs, (Australia's) Peter Siddle the other day bowled 60.
"Can Malinga do that? I don't think so. I don't think we can make that decision and risk his career."
Team: Tillakaratne Dilshan, Dimuth Karunaratne, Kumar Sangakkara, Mahela Jayawardene (captain), Thilan Samaraweera, Angelo Mathews, Prasanna Jayawardene, Nuwan Kulasekara, Chanaka Welegedera, Shaminda Eranga, Rangana Herath.
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