Head has been battling to recover from a hamstring strain, and was still uncertain over his status to play less than 24 hours from the first ball.
It's understood that Glenn Maxwell is on standby to play what would be his first red ball fixture since before the onset of the coronavirus pandemic should he fail to pass fitness.
Galle is a finger spin paradise, which was set to bring Jon Holland into the side for Swepson, however he has not been considered due to a finger injury, while Ashton Agar is also out with a side strain.
Holland was due to play for Australia A last week, but suffered a cut to his finger in training and is yet to return to the field.
It has left the Aussies needing to rely on Swepson to play, but Cummins told the media that they were "really happy" with the way he has been bowling.
"We're really happy with 'Swepo'," he said.
"He is bowling beautifully and really ready for this one.
"These conditions … it's quite different to what we experience in Australia. That's the challenge of trying to win overseas.
"A lot of our preparation work has been around trusting our own methods. We might go about it a little bit differently to how Sri Lanka will."
"I think his role here might be slightly different as well," Cummins added.
"Pakistan we knew was going to be a slow grind and I thought he did his job despite not taking the wickets he would like. He was a really important cog in that bowling engine.
"It's always exciting having a leggie in the side as a captain. It feels like a real luxury to throw him the ball and see him go about it."
The first Test against Sri Lanka starts at 2:30pm (AEST) today, with the hosts likely to play up to three spinners in their side.
Likely Australian XI
1. David Warner
2. Usman Khawaja
3. Marnus Labuschagne
4. Steve Smith
5. Travis Head (Glenn Maxwell if not fit)
6. Cameron Green
7. Alex Carey (wk)
8. Pat Cummins
9. Mitchell Starc
10. Nathan Lyon
11. Mitchell Swepson