Arsenal will play Rennes in the last 16 of the Europa League while Chelsea will face Dynamo Kiev.
Chelsea will have home advantage in the first leg against the Ukranian side, while Arsenal will travel to France first on March 7.
Arsenal beat BATE 3-1 on aggregate to reach the last 16 and their reward is a tie with Rennes, who eliminated Real Betis in the previous round.
The French side sit 11th in Ligue 1 and their squad includes former Newcastle and Hull winger Hatem Ben Arfa.
Chelsea, winners of this competition in 2013, defeated Malmo, winning the second leg 3-0 at Stamford Bridge on Thursday to add to a 2-1 away triumph in Sweden.
Friday's draw was not protected by any seeding, but teams from Russia and Ukraine were kept apart.
Elsewhere, Eintracht Frankfurt of Germany were paired with Serie A side Inter Milan, Dinamo Zagreb will play Portuguese outfit Benfica, while Napoli tackle Austria's Red Bull Salzburg.
Valencia, who knocked out Celtic, have been pitted against Russian club Krasnodar, while five-times winners Sevilla face Slavia Prague and Zenit St Petersburg play Villarreal.
Europa League round of 16 draw
Chelsea v Dynamo Kiev
Eintracht Frankfurt v Inter Milan
Dinamo Zagreb v Benfica
Napoli v Salzburg
Valencia v Krasnodar
Sevilla v Slavia Prague
Arsenal v Rennes
Zenit St Petersburg v Villarreal
First legs will be played on March 7, second legs on March 14