William was joined by club ambassador Ahmed Elmohamady in the Villa Park stands in Birmingham.
Chris Wood’s penalty in the first leg had given Vitor Pereira’s Forest side the edge but Ollie Watkins levelled the aggregate scores in the 36th minute.
Forest failed to deliver the type of performance that saw them go 10 games unbeaten and they went behind in the tie 13 minutes after the interval, courtesy of Emi Buendia’s penalty, before John McGinn’s double sealed a 4-1 aggregate win and a trip to Istanbul.
William, patron of the Football Association, is a passionate Villa supporter and has followed the Midlands club since he was a schoolboy.
He was born less than a month after Villa’s most famous continental success, when they beat Bayern Munich to lift the European Cup in May 1982.
It is not yet known whether the prince will travel to Istanbul for the final later this month.