Sinckler appeared before a hearing via video conference on Tuesday and denied that he had committed any foul play.
Sinckler was cited "for an act of foul play contrary to Law 9.12 [biting] during the 64th minute of the second test against South Africa in Cape Town on 31 July, 2021," a statement from World Rugby said on Sunday.
"The player denied that he had committed an act of foul play worthy of a red card. Having reviewed all the evidence, the committee deemed that on the balance of probabilities, it could not be satisfied that the player committed an act of foul play. On that basis, the committee dismissed the citing and the player is free to play again immediately," the independent judicial committee said in a statement.
If he had been found guilty, the England front-row forward could have faced a sanction of anything between three months and two years on the sidelines.
Media reported the prop was alleged to have bitten South Africa second-row Franco Mostert's arm during a ruck at the Cape Town Stadium during the South Africa's 27-9 victory.
Gatland on Tuesday named Sinckler among the replacements again for Saturday's decisive third test, subject to the outcome of the hearing.