"Following examination of all the evidence, notably the declarations of both the referee and the referees’ assessor, as well as the various video footage, it was not established to the panel’s satisfaction that the referee had been deceived in taking his decision on the penalty," UEFA said in a statement on its official website.
The Croatian is now free to feature in their opening Group H clash away to Standard Liege on Wednesday.
"I'm very pleased that we have finally arrived at the truth," said Eduardo in a statement on the Arsenal website.
"All we needed to do was to prove what happened and we have managed to do that. This decision makes me feel a lot better.
"I just want to say that I'm a fair player. To score goals you must take your opportunities and I'm not the type of player who needs to be dishonest to score goals."
The Gunners also welcomed Uefa's decision.
"We were able to show there was contact between the keeper and Eduardo and that the decision should be annulled," said a Gunners statement.
"We fully support the drive for fair play in football and believe it is important that Uefa provides clear and comprehensive standards that will be consistently enforced going forward.
"We are glad to put this incident behind us and concentrate on the games ahead."