Premat and Moffat join Thomas Randle, who was confirmed to make his Tickford return late last year.
Should Premat return to Australia, he will face mandatory quarantine before being able to link up with Tickford.
He tested with the team in February last year, before returning to Stateside.
Tickford CEO and team principal Edwards said the 2019 Bathurst winner is ready to make his return, having missed the 2020 race altogether.
"Fortunately international travel restrictions are starting to open up which gives us the chance to bring Alex over," Edwards said.
"We'll go through the necessary steps to secure a travel exemption, and Alex is prepared to do his 14 days of quarantine, testing, and everything else involved to come over.
"He’ll get some seat time at our regular enduro test, then we'll head to Bathurst and go for it."
Premat won the 2019 Great Race with Scott McLaughlin and DJR Team Penske, before he was dropped in favour of Tim Slade.
Tickford will determine its driver pairings for the Bathurst 1000 at a later date.
The team downsized to three cars for 2021, with Cameron Waters, Jack Le Brocq and James Courtney returning.
Premat will not attend the team's pre-season test at Winton Motor Raceway on Friday.
However, Moffat and Randle will have the chance to reacquaint with the team's Mustangs ahead of the season-opening Repco Mount Panorama 500.
"Finally. I'm mega delighted to come back to the Bathurst 1000," Premat said.
"I missed it so much last year and I am ready to put my hat in the ring this season.
"I'm very motivated to come back, especially after seeing how well the Tickford team did in 2020.
"I can't wait to get back to Australia later this year and I’m looking forward to the challenge."
Tickford's three cars will be on track at Winton for Friday's official pre-season test.