The UK Airprox Board said the two aircraft came within 100ft of each other and one of the pilots had been forced to "duck under" the other jet.
A report said the controller was "relatively inexperienced".
The incident happened on 26 November last year.
A near miss involving two RAF Tornado jets near Lossiemouth has been put down to a misjudgement by an inexperienced member of staff in the control tower.