Smith's availability had been in doubt when he hurt his right elbow throwing in the field during the Sydney Sixers' washed-out Big Bash League derby against the Sydney Thunder on Friday night.
The injury came only 10 days out from the first of two matches in Galle, where Smith was named captain as Pat Cummins opted to stay home for the birth of his child.
Cricket Australia delayed Smith's flight to the Australian team's preparation camp in Dubai to consult with a specialist, and on Monday, received good news about the elbow on which he previously had surgery.
The 35-year-old has been cleared to fly to the UAE, where the Test squad has congregated at the ICC Academy to prepare for the humid conditions and turning pitches they will face in Sri Lanka.
"Smith is expected to return to batting later in the week to begin his preparation for the first Test against Sri Lanka," a Cricket Australia statement read.
Steve Smith is on track to play the first Test. (Mark Evans/AAP PHOTOS)
Named vice-captain for the series, Travis Head had been expected to become Australia's 48th Test captain if Smith failed to pull up in time.Â
But veteran batter Smith now returns to captain his first full series since the 2018 Newlands ball-tampering saga.
Smith's injury comes as spinner Matthew Kuhnemann hopes to prove his fitness for the series after undergoing surgery on a thumb injury to his non-bowling hand suffered in the BBL.
Kuhnemann's departure from Australia has also been delayed, but the 28-year-old is expected to resume bowling later this week with a view to joining the squad in Sri Lanka.
Travis Head will be vice-captain of the Australian Test team in Sri Lanka. (Dan Himbrechts/AAP PHOTOS)
Ahead of the BBL finals, Test legend David Warner nominated Thunder teammate and left arm off-spinner Tom Andrews as an out-of-the-box replacement should Kuhnemann fail to recover.
He was less sold on suggestions 21-year-old allrounder Cooper Connolly could operate as a front-line spinner in Kuhnemann's absence.
"Connolly (would) have to bowl 25 overs ... they could throw someone like Tommy Andrews over there as well," Warner said.
"You've got a good back-up there in Todd Murphy. It is two bowlers (Murphy and Nathan Lyon) bowling the same (offspin) but when you've got quality, you might as well use it."
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