The SFA said in a statement that a "notice of complaint" had been dismissed and no suspension would be applied after Inverness had contested the offer of a one-game ban.
Meekings blocked a goalbound header with his arm during Sunday's semi-final which Inverness won 3-2 to reach the final for the first time.
Referee Steven McLean and his assistants missed the incident, but the Scottish FA's compliance officer Tony McGlennan issued a notice of complaint.
"The result means that the club can now fully appreciate the achievement of reaching its first ever Scottish Cup final and focus on preparations for Saturday's game versus Aberdeen FC," Inverness chairman Kenny Cameron said on the club website.
"On a personal note, both Josh and I would like to express our gratitude to our legal team from Harper Macleod led by Partner David Kerr who worked tirelessly to ensure a favourable outcome."
FIFA's referee chief Jim Boyce told Reuters on Wednesday that he was opposed to the intervention by the compliance officer because it sets a "very dangerous precedent".
Celtic manager Ronny Deila also said he hoped Meekings escaped a ban because he did not believe the defender handled the ball on purpose.
(Reporting By Michael Hann; editing by Toby Davis)
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