Everton will face Dynamo Kiev in the last 16 of the Europa League while holders Sevilla were drawn against fellow Spaniards Villarreal.
Roberto Martinez's side booked their place in the last 16 with a comfortable two-legged win over Swiss outfit Young Boys. Leading 4-1 from the first leg in Switzerland, courtesy of a Romelu Lukaku hat-trick, the Toffees secured a second win over their opponents with a 3-1 victory at Goodison Park - Lukaku again scoring a further two goals.
The Premier League side will now face Ukrainian outfit Dynamo Kiev for a place in the quarter-finals. The first leg will be played on Merseyside before the Toffees travel to Kiev to play at the Olimpiyskiy Sports Complex.
Defending champions Sevilla were paired with La Liga rivals Villarreal while another highlight of the draw was an all-Italian clash between Fiorentina and Roma.
Country protection does not apply at this stage of the competition but Russian and Ukrainian teams were kept apart due to the ongoing instability in the region.
That saw the two Ukrainian sides separated from the main pots and Europa League ambassador Jerzy Dudek drew Everton against Dynamo, who had been placed in the first tie. Dnipro were then paired with 1992 champions Ajax in the second.
Proceedings then continued as an open, unseeded draw, with Russian side Zenit St Petersburg next out and drawn against Torino. Dinamo Moscow, the fourth side affected by UEFA's stipulation, will face 1989 UEFA Cup champions Napoli.
Bundesliga side Wolfsburg were pitted against three-times champions Inter Milan in another appealing tie, while Belgian league leaders Club Brugge face Turkey's Besiktas.
The ties will be played on March 12 and 19.
Everton v Dynamo Kiev
Dnipro Dnipropetrovsk v Ajax Amsterdam
Zenit St Petersburg v Torino
VfL Wolfsburg v Inter Milan
Villarreal v Sevilla
Napoli v Dinamo Moscow
Club Bruges v Besiktas
Fiorentina v AS Roma