Symons was on the bench alongside Chris Coleman for Friday night’s memorable 1-0 European Qualifier victory over Belgium in Cardiff.
He had been in position as Wales No 2 since January 2012 before continuing employment with his country after succeeding the sacked Felix Magath at Craven Cottage.
Symons leaves Wales in rude health, top of Group B after beating the Belgians, and with a strong chance of qualifying for a first major tournament since 1958.
Symons was capped 37 times by Wales during his playing career and was permanently appointed in the Fulham position in October after impressing in an interim role, signing a deal until the summer of 2016 after the club took 13 points from a possible 21.
The south Londoners eventually finished 17th in the Championship table, 11 points above the relegation zone.