"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 the referee had been deceived in taking his decision on the penalty," said UEFA in a statement on Monday.
"Therefore the decision of the UEFA control and disciplinary body of September 1, in which the player was suspended for two UEFA club competition matches, is annulled," added European football's ruling body.
The Brazilian-born Croatian international was initially banned after winning a controversial penalty against Celtic.
Eduardo went down in the area after poking the ball past goalkeeper Artur Boruc, who dived at his feet but appeared to make little or no contact.
BROKEN LEG
The striker, who spent a year out of the game after suffering a broken leg in February 2008, converted the penalty to put Arsenal 1-0 ahead and 3-0 up on aggregate.
The Londoners eventually won 3-1 for a 5-1 aggregate victory.
"I'm very pleased we have finally arrived at the truth," Eduardo told his team's website. "All we needed to do was prove what happened and we have managed to do that.
"This decision makes me feel a lot better. I certainly feel relieved now.
"All I remember of the incident is that as soon as I had possession of the ball I headed towards goal at full speed. I was very close to the Celtic keeper and felt contact on my foot and then lost my balance," added Eduardo.
"I know perhaps more than anyone else that when you have contact at speed it can be dangerous.
"I just want to say I'm a fair (honest) 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 decision to take action against Eduardo infuriated Arsenal manager Arsene Wenger who described it as "disgraceful", accusing UEFA of launching a witch hunt against his striker.
Eduardo is now free to play in Arsenal's first two Group H matches at Standard Liege on Wednesday and at home to Olympiakos Piraeus on September 29.
