Most of the two-legged ties will be played on the 14 and 21 February 2019.
Arsenal’s home second leg will be on Wednesday, 20 February at 17:00 GMT.
The Gunners and Chelsea were both seeded for the draw, meaning they host their second legs and teams from the same city cannot play at home on the same night.
The timing of the fixture is to avoid a clash with the Champions League games taking place later on that Wednesday.
Celtic, who were beaten by Russian side Zenit St Petersburg in last 32 stage last season, last played Valencia in the Uefa Cup in 2001, with the Glasgow side losing on penalties at home in the third round.
The Bhoys finished as runners-up in their group behind Red Bull Salzburg, who beat them in the final game.
Arsenal and Chelsea both finished top of their respective groups, each winning five and drawing one of their six matches.
The Gunners are facing the same opponent they met in the group stage of last season’s competition, winning twice – 4-2 in Belarus and 6-0 in London.
Europa League last-32 draw in full
Viktoria Plzen v Dinamo Zagreb
Club Brugge v Red Bull Salzburg
Rapid Vienna v Inter Milan
Slavia Prague v Genk
Krasnodar v Bayer Leverkusen
FC Zurich v Napoli
Malmo v Chelsea
Shakhtar Donetsk v Eintracht Frankfurt
Celtic v Valencia
Rennes v Real Betis
Olympiakos v Dinamo Kiev
Lazio v Sevilla
Fenerbache v Zenit St Petersburg
Sporting Lisbon v Villarreal
Bate Borisov v Arsenal
Galatasaray v Benfica
