Stoke's first Europa League tie has them paired with Croatian giants Hajduk Split in the third qualifying round.
The first leg taking place at the Britannia Stadium on July 28 before the FA Cup runners-up travel to Split on August 4.
Hajduk have reached the quarter-finals of the European Cup three times, most recently in 1994-95, while they were semi-finalists in the UEFA Cup in 1983-84.
Potters boss Tony Pulis told the club's official website: "It's a fantastic draw for us and an occasion that every single one of us are looking forward to.
"Hajduk Split are a hugely renowned football club with great tradition in European competitions, and it's also a lovely city for our supporters to go out and visit.
"The draw has only just been made but already my phone hasn't stopped ringing - you can sense the excitement building.
"It would be absolutely fantastic to get a full house at the Britannia Stadium and get the place rocking as we host European football here for the first ever time."