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Wales had invoked a Fifa rule which meant that Savage could be called up four days before the match.
However, Fifa have now declared that Savage can report only 48 hours before the tie, as it is taking place in a week designated for friendly internationals.
Savage said: "Playing two games in four days will not be a problem.
"I'm just delighted that it has been sorted out. I've been in the middle and I've left it to the authorities to sort this matter out.
"I've understood the views of both parties.
"I want to help Birmingham hopefully get some more points in our bid to stay in the Premiership. I also want to play a part in helping Wales get to the European Championship finals in 2004."
Savage will now play against Fullham before meeting up with the rest of the Wales squad in Cardiff the same evening and then fly out to Azerbaijan the following day.
Blues chairman David Gold said: "I am thrilled that common sense has prevailed.
"I would also stress that we wish Wales all the best and want them to get to the Euro finals, but it's about having a relationship between club and country, not a war."
