Aberdeen will take on Burnley while Rangers face a trip to Macedonia and Hibernian are up against Faroe Islands opposition in Europa League qualifying.
The Dons take on the English Premier League side in the second round of qualifying, a round later than their Scottish Premiership counterparts.
Steven Gerrard's first competitive game as Rangers manager will be at home to Shkupi in their first-round tie.
On the same night, 12 July, Hibs host their first leg against Runavik.
Burnley will be playing in European competition for the first time in 51 years and Aberdeen manager Derek McInnes described it as "a fantastic draw".
The Clarets secured their place in Europe for the first time since they reached the Fairs Cup quarter-finals in 1967 by finishing seventh last season's Premier League.
"We'll be playing against a team that has done exceptionally well in what is regarded as the best league in the world," McInnes, whose side were knocked out at the third qualifying stage by Apollon Limassol of Cyprus last season, told his club website.
"It should be a fabulous contest, there are favourites in every tie and they're seeded for a good reason.
"We know we'll be big underdogs for this one. But, rest assured, we'll be doing all we possibly can to cause an upset.
"There will be a terrific atmosphere at Pittodrie and I wouldn't be surprised if it's a sell-out."
Aberdeen, runners-up in Scotland for the last four seasons, are at home for their first leg on 26 July, with the return a week later at Turf Moor.
Should Neil Lennon's side and Rangers join Aberdeen in the second round, they face awkward opposition.
The winners of Rangers' tie will take on Petrocub of Moldova or Osijek, the Croatian side who were seeded in Wednesday's draw and beat PSV Eindhoven home and away to reach the play-off round last season.
Austria Vienna denied Osijek a place in the group stage on away goals after a 2-2 draw on aggregate.
However, Rangers must first overcome Shkupi, based in the Macedonian capital of Skopje, who finished fourth in their domestic league last season and who will host the second leg on 19 July.
Hibs, who finished fourth in the Scottish Premiership last season, will be strong favourites to win their opening tie.
Runavik finished fourth last year in the Faroe Islands Premier League and currently sit third after 14 games of this campaign.
In their 11 previous European campaigns, they have never made it beyond the first qualifying round.
Awaiting the winners are Asteras Tripolis, who finished fifth in last season's Greek Superleague.
In their last foray into Europe, Hibs were beaten on penalties by Danish opposition and manager Lennon told his club website: "Against Brondby a few years ago, it was my first game in charge and we hadn't had much time to prepare, whereas the squad is more settled and we have the experience of those ties to call upon.
"We'll be up against a side midway through their league season, so they'll obviously be well prepared. We can't afford to be complacent."
Hibs and Rangers, who finished third in the Premiership under previous manager Graeme Murty, will have to negotiate four rounds of qualifying to reach the group stage.
Gerrard will hope to fare better than predecessor Pedro Caixinha, who watched his side fall at the first qualifying hurdle to Progres Niederkorn of Luxembourg a year ago.