The pair collided after a heated exchange on Sunday during the fourth day's play and were charged by the on-field umpires.
Both players had pleaded not guilty and match referee Jeff Crowe cleared them of the charges following separate hearings.
"I am satisfied in respect of both players that their physical contact was not deliberate," Crowe said in a statement. "Both players, however, could have done more to avoid each other and they have been so counselled.
"We do not condone physical contact, but recognise that on occasions such contact could be accidental."
Australia won the second test by 218 runs on Monday to take a 2-0 lead in the five-match Ashes series.
(Additional reporting by Sudipto Ganguly; Editing by Patrick Johnston)
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