After finishing in seventh place in last season’s Premier League, Everton earned themselves a return to Europe for the first time since the 2014-15 campaign.
They must come through two ties to reach the group stages of the Europa League, with Slovakian side Ruzomberok or Norwegian outfit Brann standing in their way later this month.
Brann are favourites to come through that contest having already established a 1-0 advantage from their away leg, and they will travel to Goodison Park on July 27 should they avoid defeat in the reverse fixture.
Aberdeen face a potential clash with either Apollon Limassol or Zaria Balti, but they are currently locked at 1-1 with Siroki Brijeg ahead of a trip to Croatia.
Elsewhere in the draw, AC Milan were paired with CSU Craiova and Athletic Bilbao will face Dinamo Bucharest .