The Gunners signed the Brazil-born Croatia striker from Dinamo Zagreb following the sale of captain Thierry Henry.
However, because he had not met the criteria of 75% of international appearances over the past two years, his application for a work permit went to an appeal.
With the formalities of the deal - understood to be worth £8million - the 24 year old is now free to continue his pre-season preparations with the Gunners.
Arsene Wenger had been "optimistic" of a successful appeal.
"In our first attempt they strictly applied the rule," he said at the weekend, when Arsenal won the Emirates Cup.
"Eduardo has played 50% of national team games for Croatia. I consider it a fantastic achievement at the age of 24 - and he played every single game in the last year."