Both players were charged under the International Cricket Council's Code of Conduct, which refers to "inappropriate and deliberate physical contact between players in the course of play during an international match" during the fourth day's play on Sunday.
The incident occurred in the 84th over of England's second innings when the players collided as Stokes was making a run.
Both players pleaded not guilty to the charge and separate hearings were held after the second Test on Monday, following which match referee Jeff Crowe cleared them of the charges.
"Both players, however, could have done more to avoid each other and they have been so counselled.
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"We do not condone physical contact, but recognise that on occasions such contact could be accidental."
The charges were laid by field umpires Kumar Dharmasena and Marais Erasmus and TV umpire Tony Hill.
Had the players been found guilty they would have faced a minimum fine of 50 percent of their match fees and/or up to two suspension points.