Darren Sarll's U18s will welcome the Toffees to The Lamex Stadium on Tuesday 9th December (7pm KO).
Only the West Stand will be open for this game and prices on the turnstiles will be £5 adults and £2 concessions (over-60s and under-16s).
Stevenage beat Needham Market 4-3 in Round 1 and then Wealdstone (6-0) in Round 2 to reach the third round. Meanwhile Everton, who won the FA Youth Cup in 1998, reached the quarter-finals of last year's competition before losing 3-1 at The Emirates to Arsenal.
You can watch all the goals from Stevenage's 6-0 win against Wealdstone below!