Sachs, who was appointed late Friday, will hear the case within a week, the International Cricket Council (ICC) said in a statement released late Saturday.
"The ICC received official notification of the appeal from the Board of Control for Cricket in India (BCCI) on Friday," the statement said.
"The ICC Head of Legal, David Becker, appointed Justice Sachs later the same evening in accordance with ICC Code of Conduct processes."
The Indian opener can continue to play pending the outcome of the appeal.
Gambhir was banned by match referee Chris Broad for "physical contact" with Shane Watson while taking a run on the first day of the match.
The Australian all rounder was fined 10 percent of his match fee for "verbally engaging" with the Indian opener, who scored 206 in India's first innings here.
Gambhir, 27, appeared to elbow Watson after the all-rounder seemed to mutter something to the Indian batsman as he took a second run in the 51st over of Wednesday's play.
Soon after the ban was announced, the Indian Cricket Board lodged the appeal on Gambhir's behalf.
Justice Sachs has the power "to increase, decrease, amend or otherwise substitute his own decision" from that made at the previous hearing, and his decision would be final and binding.
The players were cited by on-field umpires Billy Bowden and Aleem Dar as well as TV umpire Suresh Shastri.
Watson had pleaded not guilty to a level one violation of the ICC Code of Conduct, which calls on players to respect the laws and spirit of the game.
Gambhir pleaded guilty to a level two offence of conduct contrary to the spirit of the game.
The Indian opener was fined 65 percent of his match fee during the Kanpur one-dayer against Pakistan in November 2007 for a run-in with Shahid Afridi.
India's paceman Zaheer Khan was docked 80 percent of his match fee after exchanging words with Matthew Hayden and pointing him to the pavilion during the second Test of a tense series in Mohali.
The series, which the hosts lead 1-0 after a 320-run win in Mohali, comes on the heels of India's acrimonious tour of Australia early this year.
The fourth and final Test starts in Nagpur on Thursday.