Viborg followed up their 3-0 first-leg win over B36 Torshavn last week with a 2-1 triumph in the return game on Tuesday night, comfortably progressing to the next round 5-1 on aggregate.
The Hammers are now scheduled to face Viborg at the London Stadium in the first leg on August 18, before travelling to Denmark for the reverse fixture a week later.
David Moyes's side enjoyed a memorable run to the Europa League semi-finals last season before losing out to eventual winners Eintracht Frankfurt over two legs.
However, following their seventh-place finish in the Premier League last term, West Ham will now attempt to qualify for the second edition of the Europa Conference League.
The Hammers will come up against a Viborg side who finished seventh in the Danish Superliga last season and currently sit in the same position after four games this term.
Elsewhere, Rangers will face PSV Eindhoven in a Champions League playoff tie following an impressive comeback victory over Union SG, winning 3-0 in the second leg at Ibrox on Tuesday night to progress 3-2 on aggregate.
Fellow Scottish side Hearts will face either FC Zurich or Linfield in a Europa League playoff tie, while Dundee United will set up a Europa Conference League playoff clash with either Riga FC or Gil Vicente if they can edge through their third-round qualifier against AZ Alkmaar, who currently trail 1-0 to the Tangerines from the first leg.
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