The stand-in captain beat out the series' leading wicket-taker Matt Kuhnemann (16 scalps at 17.18) to claim the honour after Australia clinched a nine-wicket win in the second Test in Galle.
Smith underlined his status as Australia's master of the subcontinent, scoring two centuries from as many innings to help the tourists seal a first series win in Sri Lanka since 2011.
The 35-year-old remains unsure whether he will play on Australia's next tour of the subcontinent to India in 2027, when he will be 37.
"I'm enjoying it at the moment, so I'll keep playing, keep enjoying it and take it day by day," Smith said.
An apparent recurrence of Smith's elbow injury shaped as a worrying postscript, with an already depleted Australia heading to Pakistan for the Champions Trophy this month.
Smith appeared to hyper-extend the elbow he injured in last month's Big Bash League mishap that delayed his flight to Dubai for the Test squad's training camp.
On Sunday's day four, he pulled up sore after throwing from point and tried to shake out the issue as he remained fielding.
"I threw one when I shouldn't have. There was nothing on. (It's) hard when you're in the moment to pull yourself back," he said.Â
Smith was in clear discomfort after the throw, but insisted he would bounce back for the Champions Trophy, where he could captain Australia in Pat Cummins' absence.
"It's better than it was a couple of weeks ago after the Big Bash. Pretty sure it'll be a pretty quick recovery,'' he said.
The news will be a relief to Australia, with Cummins (ankle), Mitch Marsh (back), Josh Hazlewood (side) and Marcus Stoinis (retirement) already unavailable for the 50-over tournament.
In Sri Lanka, Smith made 272 runs at an average of 136 to finish as the second-top run-scorer in the series.
He blasted 141 runs in his first knock as Australia made the most of winning the toss in the first Test, slapping their way to victory by an innings and 242 runs.
But his second ton (131) was arguably more important in the second match as Australia sought to close out a series whitewash.
Smith came to the crease when Australia were in trouble at 2-37 on day two, having lost both Travis Head and Marnus Labuschagne cheaply.
He stabilised the tourists' reply to Sri Lanka's 257 and forged a 259-run partnership with Alex Carey (156) that ultimately proved decisive in the closer second match.
It's been quite the turnaround for Smith, who was lukewarm in his stint as an opener to finish the 2023-24 summer, and managed only 19 runs across his first three innings in the recent home series against India.
But Smith has now scored centuries in four of his past five Tests.
"Even when I wasn't getting the runs I wanted, I was still saying to all you guys (the media) that I was actually batting quite nicely," Smith said.
"There's certainly a lot of luck involved, particularly in these conditions.
"You've got to make the most of it, which I've done, I suppose, in the last little bit."
Smith watched as records tumbled during the Sri Lanka series.
On day one of the first Test, he reached the coveted 10,000-run milestone after memorably finishing the home summer one run short.
During the second Test, Smith also became Australia's leading run-scorer in Asia with 1994 runs, and the first non-wicketkeeping Australian to reach 200 catches.
Additionally, the right-hander has scored more centuries (seven) in Asia than any of his countrymen.
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